swift. AVPlayer. How to track when song finished playing?

You need to create an object that implements the AVAudioPlayerDelegate protocol, and use that as the delegate of the AVAudioPlayer object. Then link them together, for example:

audioPlayer = try! AVAudioPlayer(contentsOf: audioFileUrl)
audioPlayer.delegate = self

The delegate can implement methods that responds to certain events. This one fires when the audio finishes playing:

func audioPlayerDidFinishPlaying(_ player: AVAudioPlayer, successfully flag: Bool) {
    // ...
}

Another version for Swift 3

NotificationCenter.default.addObserver(self, selector: #selector(self.playerDidFinishPlaying(sender:)), name: NSNotification.Name.AVPlayerItemDidPlayToEndTime, object: item)

func playerDidFinishPlaying(sender: Notification) {

    // Do Something
}

for Swift 4.2

func play(url: URL) {
    let item = AVPlayerItem(url: url)
    NotificationCenter.default.addObserver(self, selector: #selector(self.playerDidFinishPlaying(sender:)), name: NSNotification.Name.AVPlayerItemDidPlayToEndTime, object: item)

    let player = AVPlayer(playerItem: item)
    player.play() 
}

@objc func playerDidFinishPlaying(sender: Notification) {
    // Your code here
}

Something like this works:

func play(url: NSURL) {
    let item = AVPlayerItem(URL: url)

    NSNotificationCenter.defaultCenter().addObserver(self, selector: "playerDidFinishPlaying:", name: AVPlayerItemDidPlayToEndTimeNotification, object: item)

    let player = AVPlayer(playerItem: item)
    player.play()
}

func playerDidFinishPlaying(note: NSNotification) {
    // Your code here
}

Don't forget to remove the observer when you're done (or in deinit)!