Aqui está um exemplo que mostra como fazer sync & async.

import Foundation

class HttpDownloader {

    class func loadFileSync(url: NSURL, completion:(path:String, error:NSError!) -> Void) {
        let documentsUrl =  NSFileManager.defaultManager().URLsForDirectory(.DocumentDirectory, inDomains: .UserDomainMask).first as! NSURL
        let destinationUrl = documentsUrl.URLByAppendingPathComponent(url.lastPathComponent!)
        if NSFileManager().fileExistsAtPath(destinationUrl.path!) {
            println("file already exists [\(destinationUrl.path!)]")
            completion(path: destinationUrl.path!, error:nil)
        } else if let dataFromURL = NSData(contentsOfURL: url){
            if dataFromURL.writeToURL(destinationUrl, atomically: true) {
                println("file saved [\(destinationUrl.path!)]")
                completion(path: destinationUrl.path!, error:nil)
            } else {
                println("error saving file")
                let error = NSError(domain:"Error saving file", code:1001, userInfo:nil)
                completion(path: destinationUrl.path!, error:error)
            }
        } else {
            let error = NSError(domain:"Error downloading file", code:1002, userInfo:nil)
            completion(path: destinationUrl.path!, error:error)
        }
    }

    class func loadFileAsync(url: NSURL, completion:(path:String, error:NSError!) -> Void) {
        let documentsUrl =  NSFileManager.defaultManager().URLsForDirectory(.DocumentDirectory, inDomains: .UserDomainMask).first as! NSURL
        let destinationUrl = documentsUrl.URLByAppendingPathComponent(url.lastPathComponent!)
        if NSFileManager().fileExistsAtPath(destinationUrl.path!) {
            println("file already exists [\(destinationUrl.path!)]")
            completion(path: destinationUrl.path!, error:nil)
        } else {
            let sessionConfig = NSURLSessionConfiguration.defaultSessionConfiguration()
            let session = NSURLSession(configuration: sessionConfig, delegate: nil, delegateQueue: nil)
            let request = NSMutableURLRequest(URL: url)
            request.HTTPMethod = "GET"
            let task = session.dataTaskWithRequest(request, completionHandler: { (data: NSData!, response: NSURLResponse!, error: NSError!) -> Void in
                if (error == nil) {
                    if let response = response as? NSHTTPURLResponse {
                        println("response=\(response)")
                        if response.statusCode == 200 {
                            if data.writeToURL(destinationUrl, atomically: true) {
                                println("file saved [\(destinationUrl.path!)]")
                                completion(path: destinationUrl.path!, error:error)
                            } else {
                                println("error saving file")
                                let error = NSError(domain:"Error saving file", code:1001, userInfo:nil)
                                completion(path: destinationUrl.path!, error:error)
                            }
                        }
                    }
                }
                else {
                    println("Failure: \(error.localizedDescription)");
                    completion(path: destinationUrl.path!, error:error)
                }
            })
            task.resume()
        }
    }
}

Aqui está como usá-lo no seu código:

let url = NSURL(string: "http://www.mywebsite.com/myfile.pdf") 
HttpDownloader.loadFileAsync(url, completion:{(path:String, error:NSError!) in
                println("pdf downloaded to: \(path)")
            })

Por favor, note que eu liguei os "modos de fundo / obtenção de fundo" em "capacidades".

Uma vez que o completionhandler não era suportado, a solução não é sintetizar. Sinto muito por isso.

--Swift 2.3 --

import Foundation 
class Downloader : NSObject, NSURLSessionDownloadDelegate
{
    var url : NSURL? 
    // will be used to do whatever is needed once download is complete
    var yourOwnObject : NSObject?

    init(yourOwnObject : NSObject)
    {
        self.yourOwnObject = yourOwnObject
    }

    //is called once the download is complete
    func URLSession(session: NSURLSession, downloadTask: NSURLSessionDownloadTask, didFinishDownloadingToURL location: NSURL)
    {
        //copy downloaded data to your documents directory with same names as source file
        let documentsUrl =  NSFileManager.defaultManager().URLsForDirectory(.DocumentDirectory, inDomains: .UserDomainMask).first
        let destinationUrl = documentsUrl!.URLByAppendingPathComponent(url!.lastPathComponent!)
        let dataFromURL = NSData(contentsOfURL: location)
        dataFromURL?.writeToURL(destinationUrl, atomically: true)

        //now it is time to do what is needed to be done after the download
        yourOwnObject!.callWhatIsNeeded()
    }

    //this is to track progress
    func URLSession(session: NSURLSession, downloadTask: NSURLSessionDownloadTask, didWriteData bytesWritten: Int64, totalBytesWritten: Int64, totalBytesExpectedToWrite: Int64)
    {
    }

    // if there is an error during download this will be called
    func URLSession(session: NSURLSession, task: NSURLSessionTask, didCompleteWithError error: NSError?)
    {
        if(error != nil)
        {
            //handle the error
            print("Download completed with error: \(error!.localizedDescription)");
        }
    }

    //method to be called to download
    func download(url: NSURL)
    {
        self.url = url

        //download identifier can be customized. I used the "ulr.absoluteString"
        let sessionConfig = NSURLSessionConfiguration.backgroundSessionConfigurationWithIdentifier(url.absoluteString)
        let session = NSURLSession(configuration: sessionConfig, delegate: self, delegateQueue: nil)
        let task = session.downloadTaskWithURL(url)
        task.resume()
    }
}

    let url = NSURL(string: "http://company.com/file.txt")
    Downloader(yourOwnObject).download(url!)

--Swift 3--

class Downloader : NSObject, URLSessionDownloadDelegate {

var url : URL?
// will be used to do whatever is needed once download is complete
var yourOwnObject : NSObject?

init(_ yourOwnObject : NSObject)
{
    self.yourOwnObject = yourOwnObject
}

//is called once the download is complete
func urlSession(_ session: URLSession, downloadTask: URLSessionDownloadTask, didFinishDownloadingTo location: URL)
{
    //copy downloaded data to your documents directory with same names as source file
    let documentsUrl =  FileManager.default.urls(for: .documentDirectory, in: .userDomainMask).first
    let destinationUrl = documentsUrl!.appendingPathComponent(url!.lastPathComponent)
    let dataFromURL = NSData(contentsOf: location)
    dataFromURL?.write(to: destinationUrl, atomically: true)

    //now it is time to do what is needed to be done after the download
    yourOwnObject!.callWhatIsNeeded()
}

//this is to track progress
private func URLSession(session: URLSession, downloadTask: URLSessionDownloadTask, didWriteData bytesWritten: Int64, totalBytesWritten: Int64, totalBytesExpectedToWrite: Int64)
{
}

// if there is an error during download this will be called
func urlSession(_ session: URLSession, task: URLSessionTask, didCompleteWithError error: Error?)
{
    if(error != nil)
    {
        //handle the error
        print("Download completed with error: \(error!.localizedDescription)");
    }
}

//method to be called to download
func download(url: URL)
{
    self.url = url

    //download identifier can be customized. I used the "ulr.absoluteString"
    let sessionConfig = URLSessionConfiguration.background(withIdentifier: url.absoluteString)
    let session = Foundation.URLSession(configuration: sessionConfig, delegate: self, delegateQueue: nil)
    let task = session.downloadTask(with: url)
    task.resume()
}}

    let url = URL(string: "http://company.com/file.txt")
    Downloader(yourOwnObject).download(url!)

Se precisar de transferir apenas o ficheiro de texto para String pode usar desta forma simples, Swift 3:

let list = try? String(contentsOf: URL(string: "https://example.com/file.txt")!)

No caso de querer resultados não opcionais ou tratamento de erros:

do {
    let list = try String(contentsOf: URL(string: "https://example.com/file.txt")!)
}
catch {
    // Handle error here
}

Você deve saber que as operações de rede podem demorar algum tempo, para evitar que corra no tópico principal e trave a sua UI, você pode querer executar o código assíncronamente, por exemplo:

DispatchQueue.global().async {
    let list = try? String(contentsOf: URL(string: "https://example.com/file.txt")!)
}

Swift 3

Queres baixar o ficheiro, bite by bite e mostrar em vista de progresso então você quer tentar este código

import UIKit

class ViewController: UIViewController,URLSessionDownloadDelegate,UIDocumentInteractionControllerDelegate {

    @IBOutlet weak var img: UIImageView!
    @IBOutlet weak var btndown: UIButton!
    var urlLink: URL!
    var defaultSession: URLSession!
    var downloadTask: URLSessionDownloadTask!
    //var backgroundSession: URLSession!
    @IBOutlet weak var progress: UIProgressView!
    override func viewDidLoad() {
        super.viewDidLoad()

        // Do any additional setup after loading the view, typically from a nib.

        let backgroundSessionConfiguration = URLSessionConfiguration.background(withIdentifier: "backgroundSession")
        defaultSession = Foundation.URLSession(configuration: backgroundSessionConfiguration, delegate: self, delegateQueue: OperationQueue.main)
        progress.setProgress(0.0, animated: false)
    }

    func startDownloading () {
        let url = URL(string: "http://publications.gbdirect.co.uk/c_book/thecbook.pdf")!
        downloadTask = defaultSession.downloadTask(with: url)
        downloadTask.resume()
    }

    @IBAction func btndown(_ sender: UIButton) {

        startDownloading()

    }

    func showFileWithPath(path: String){
        let isFileFound:Bool? = FileManager.default.fileExists(atPath: path)
        if isFileFound == true{
            let viewer = UIDocumentInteractionController(url: URL(fileURLWithPath: path))
            viewer.delegate = self
            viewer.presentPreview(animated: true)
        }

    }


    // MARK:- URLSessionDownloadDelegate
    func urlSession(_ session: URLSession, downloadTask: URLSessionDownloadTask, didFinishDownloadingTo location: URL) {

        print(downloadTask)
        print("File download succesfully")

        let path = NSSearchPathForDirectoriesInDomains(FileManager.SearchPathDirectory.documentDirectory, FileManager.SearchPathDomainMask.userDomainMask, true)
        let documentDirectoryPath:String = path[0]
        let fileManager = FileManager()
        let destinationURLForFile = URL(fileURLWithPath: documentDirectoryPath.appendingFormat("/file.pdf"))

        if fileManager.fileExists(atPath: destinationURLForFile.path){
            showFileWithPath(path: destinationURLForFile.path)
            print(destinationURLForFile.path)
        }
        else{
            do {
                try fileManager.moveItem(at: location, to: destinationURLForFile)
                // show file
                showFileWithPath(path: destinationURLForFile.path)
            }catch{
                print("An error occurred while moving file to destination url")
            }
        }



    }

    func urlSession(_ session: URLSession, downloadTask: URLSessionDownloadTask, didWriteData bytesWritten: Int64, totalBytesWritten: Int64, totalBytesExpectedToWrite: Int64) {
        progress.setProgress(Float(totalBytesWritten)/Float(totalBytesExpectedToWrite), animated: true)
    }

    func urlSession(_ session: URLSession, task: URLSessionTask, didCompleteWithError error: Error?) {
        downloadTask = nil
        progress.setProgress(0.0, animated: true)
        if (error != nil) {
            print("didCompleteWithError \(error?.localizedDescription ?? "no value")")
        }
        else {
            print("The task finished successfully")
        }
    }

    func documentInteractionControllerViewControllerForPreview(_ controller: UIDocumentInteractionController) -> UIViewController
    {
        return self
    }

    override func didReceiveMemoryWarning() {
        super.didReceiveMemoryWarning()
        // Dispose of any resources that can be recreated.
    }


}

Use este código que deseja obter automaticamente na pasta de documentos da sua aplicação

Este código funciona a 100%

Aqui está a versão Swift 4:

static func loadFileAsync(url: URL, completion: @escaping (String?, Error?) -> Void)
{
    let documentsUrl =  FileManager.default.urls(for: .documentDirectory, in: .userDomainMask).first!

    let destinationUrl = documentsUrl.appendingPathComponent(url.lastPathComponent)

    if FileManager().fileExists(atPath: destinationUrl.path)
    {
        completion(destinationUrl.path, nil)
    }
    else
    {
        let session = URLSession(configuration: URLSessionConfiguration.default, delegate: nil, delegateQueue: nil)
        var request = URLRequest(url: url)
        request.httpMethod = "GET"
        let task = session.dataTask(with: request, completionHandler:
        {
            data, response, error in
            if error == nil
            {
                if let response = response as? HTTPURLResponse
                {
                    if response.statusCode == 200
                    {
                        if let data = data
                        {
                            if let _ = try? data.write(to: destinationUrl, options: Data.WritingOptions.atomic)
                            {
                                completion(destinationUrl.path, error)
                            }
                            else
                            {
                                completion(destinationUrl.path, error)
                            }
                        }
                        else
                        {
                            completion(destinationUrl.path, error)
                        }
                    }
                }
            }
            else
            {
                completion(destinationUrl.path, error)
            }
        })
        task.resume()
    }
}

Tente este código apenas Swift 3.0 Primeiro criar um ficheiro de objectos NS Copiar este código no ficheiro criado

import UIKit

class Downloader : NSObject, URLSessionDownloadDelegate {

    var url : URL?
    // will be used to do whatever is needed once download is complete
    var obj1 : NSObject?

    init(_ obj1 : NSObject)
    {
        self.obj1 = obj1
    }

    //is called once the download is complete
    func urlSession(_ session: URLSession, downloadTask: URLSessionDownloadTask, didFinishDownloadingTo location: URL)
    {
        //copy downloaded data to your documents directory with same names as source file
        let documentsUrl =  FileManager.default.urls(for: .documentDirectory, in: .userDomainMask).first
        let destinationUrl = documentsUrl!.appendingPathComponent(url!.lastPathComponent)
        let dataFromURL = NSData(contentsOf: location)
        dataFromURL?.write(to: destinationUrl, atomically: true)

        //now it is time to do what is needed to be done after the download
        //obj1!.callWhatIsNeeded()
    }

    //this is to track progress
    private func URLSession(session: URLSession, downloadTask: URLSessionDownloadTask, didWriteData bytesWritten: Int64, totalBytesWritten: Int64, totalBytesExpectedToWrite: Int64)
    {
    }

    // if there is an error during download this will be called
    func urlSession(_ session: URLSession, task: URLSessionTask, didCompleteWithError error: Error?)
    {
        if(error != nil)
        {
            //handle the error
            print("Download completed with error: \(error!.localizedDescription)");
        }
    }

    //method to be called to download
    func download(url: URL)
    {
        self.url = url

        //download identifier can be customized. I used the "ulr.absoluteString"
        let sessionConfig = URLSessionConfiguration.background(withIdentifier: url.absoluteString)
        let session = Foundation.URLSession(configuration: sessionConfig, delegate: self, delegateQueue: nil)
        let task = session.downloadTask(with: url)
        task.resume()
    }}

Em seguida, copiar abaixo do código e colocar o código no lugar de você quer baixar o arquivo

 object = "http://www.mywebsite.com/myfile.pdf"
       let url1 = URL(string: object!)
        Downloader(url1! as NSObject).download(url: url1!)

Swift 3

class ViewController: UIViewController {
    var urlLink: URL!
    var defaultSession: URLSession!
    var downloadTask: URLSessionDownloadTask!
}

// MARK: Button Pressed
    @IBAction func btnDownloadPressed(_ sender: UIButton) {
        let urlLink1 = URL.init(string: "https://github.com/VivekVithlani/QRCodeReader/archive/master.zip")
        startDownloading(url: urlLink!)
}
    @IBAction func btnResumePressed(_ sender: UIButton) {
    downloadTask.resume()
}

@IBAction func btnStopPressed(_ sender: UIButton) {
    downloadTask.cancel()
}

@IBAction func btnPausePressed(_ sender: UIButton) {
    downloadTask.suspend()
}

    func startDownloading (url:URL) {
        let backgroundSessionConfiguration = URLSessionConfiguration.background(withIdentifier: "backgroundSession")
        defaultSession = Foundation.URLSession(configuration: backgroundSessionConfiguration, delegate: self, delegateQueue: OperationQueue.main)
        downloadProgress.setProgress(0.0, animated: false)
        downloadTask = defaultSession.downloadTask(with: urlLink)
        downloadTask.resume()
    }

// MARK:- URLSessionDownloadDelegate
func urlSession(_ session: URLSession, downloadTask: URLSessionDownloadTask, didFinishDownloadingTo location: URL) {
    print("File download succesfully")
}

func urlSession(_ session: URLSession, downloadTask: URLSessionDownloadTask, didWriteData bytesWritten: Int64, totalBytesWritten: Int64, totalBytesExpectedToWrite: Int64) {
    downloadProgress.setProgress(Float(totalBytesWritten)/Float(totalBytesExpectedToWrite), animated: true)
}

func urlSession(_ session: URLSession, task: URLSessionTask, didCompleteWithError error: Error?) {
    downloadTask = nil
    downloadProgress.setProgress(0.0, animated: true)
    if (error != nil) {
        print("didCompleteWithError \(error?.localizedDescription)")
    }
    else {
        print("The task finished successfully")
    }
}

Sim, você pode muito facilmente transferir arquivos do Url remoto usando este código. Este código está a funcionar bem para mim.

func DownlondFromUrl(){
   // Create destination URL 
let documentsUrl:URL =  FileManager.default.urls(for: .documentDirectory, in: .userDomainMask).first as URL!
let destinationFileUrl = documentsUrl.appendingPathComponent("downloadedFile.jpg")

//Create URL to the source file you want to download
let fileURL = URL(string: "https://s3.amazonaws.com/learn-swift/IMG_0001.JPG")

let sessionConfig = URLSessionConfiguration.default
let session = URLSession(configuration: sessionConfig)

let request = URLRequest(url:fileURL!)

let task = session.downloadTask(with: request) { (tempLocalUrl, response, error) in
    if let tempLocalUrl = tempLocalUrl, error == nil {
        // Success
        if let statusCode = (response as? HTTPURLResponse)?.statusCode {
            print("Successfully downloaded. Status code: \(statusCode)")
        }

        do {
            try FileManager.default.copyItem(at: tempLocalUrl, to: destinationFileUrl)
        } catch (let writeError) {
            print("Error creating a file \(destinationFileUrl) : \(writeError)")
        }

    } else {
        print("Error took place while downloading a file. Error description: %@", error?.localizedDescription);
    }
}
task.resume()
}

Use URLSessionDownloadTask para baixar os ficheiros em segundo plano, de modo a que possam ser completados mesmo que a aplicação seja terminada.

Para mais informações, ver:

Https://www.ralfebert.de/snippets/ios/urlsession-background-downloads/

Também mostra como implementar o acompanhamento do progresso para múltiplas tarefas que decorrem em paralelo: