How do I download a file in Alamofire 4 and save to the Documents directory?

Swift 3.x and Alamofire 4.x version

Well certainly the Alamofire example posted by Alamofire itself has bugs. Since fileURL returns Void it can't be used as a parameter in return statement.

Also remove .createIntermediateDirectories from option list of return statement if you don't want any Directories for the file you downloaded

EDIT
If you want to know the type of file, simply grab the last component part and convert String to NSString as NSString have these functionalities.

//audioUrl should be of type URL
let audioFileName = String((audioUrl?.lastPathComponent)!) as NSString

//path extension will consist of the type of file it is, m4a or mp4
let pathExtension = audioFileName.pathExtension

let destination: DownloadRequest.DownloadFileDestination = { _, _ in
    var documentsURL = FileManager.default.urls(for: .documentDirectory, in: .userDomainMask)[0]

    // the name of the file here I kept is yourFileName with appended extension
    documentsURL.appendPathComponent("yourFileName."+pathExtension)
    return (documentsURL, [.removePreviousFile])
}

Alamofire.download("yourAudioUrl", to: destination).response { response in
            if response.destinationURL != nil {
                print(response.destinationURL!)
            }
        }

Output is

file:///Users/rajan/Library/Developer/CoreSimulator/Devices/92B4AB6E-92C0-4864-916F-9CB8F9443014/data/Containers/Data/Application/781AA5AC-9BE7-46BB-8DD9-564BBB343F3B/Documents/yourFileName.mp3

which is the actual path of your file where it is stored.

Swift 5 - Alamofire 5.1. This is the approach.

let destination: DownloadRequest.Destination = { _, _ in
        let documentsURL = FileManager.default.urls(for: .picturesDirectory, in: .userDomainMask)[0]
            let fileURL = documentsURL.appendingPathComponent("image.png")

            return (fileURL, [.removePreviousFile, .createIntermediateDirectories])
    }

    AF.download("https://httpbin.org/image/png", to: destination).response { response in
        debugPrint(response)

        if response.error == nil, let imagePath = response.fileURL?.path {
            let image = UIImage(contentsOfFile: imagePath)
        }
    }

Why are you performing .validate? You are not storing any data after download in your current code. Alamofire allows you to store a file directly after download:

let destination: DownloadRequest.DownloadFileDestination = { _, _ in
    let documentsURL = FileManager.default.urls(for: .documentDirectory, in: .userDomainMask)[0]
    let fileURL = documentsURL.appendPathComponent("pig.png")

    return (fileURL, [.removePreviousFile, .createIntermediateDirectories])
}

Alamofire.download(urlString, to: destination).response { response in
    print(response)

    if response.result.isSuccess, let imagePath = response.destinationURL?.path {
        let image = UIImage(contentsOfFile: imagePath)
    }
}

And by the way, the download path you are providing in the download method, is the local URL to the Documents directory and not a URL of a server.