Solution for Swift 3-4 with animations and keyboard frame changing:
First, create a Bool:
// MARK: - Private Properties
private var isKeyboardShowing = false
Secondly, add Observers to the System Keyboard Notifications:
// MARK: - Overriding ViewController Life Cycle Methods
override func viewWillAppear(_ animated: Bool) {
    super.viewWillAppear(animated)
    NotificationCenter.default.addObserver(self, selector: #selector(keyboardWillShow), name: .UIKeyboardWillShow, object: nil)
    NotificationCenter.default.addObserver(self, selector: #selector(keyboardWillHide), name: .UIKeyboardWillHide, object: nil)
    NotificationCenter.default.addObserver(self, selector: #selector(keyboardWillChangeFrame), name: .UIKeyboardWillChangeFrame, object: nil)
}
Thirdly, prepare the animation function:
func adjustTableViewInsets(keyboardHeight: CGFloat, duration: NSNumber, curve: NSNumber){
    var extraHeight: CGFloat = 0
    if keyboardHeight > 0 {
        extraHeight = 20
        isKeyboardShowing = true
    } else {
        isKeyboardShowing = false
    }
    let contentInset = UIEdgeInsets(top: 0, left: 0, bottom: keyboardHeight + extraHeight, right: 0)
    func animateFunc() {
        //refresh constraints
        //self.view.layoutSubviews()
        tableView.contentInset = contentInset
    }
    UIView.animate(withDuration: TimeInterval(duration), delay: 0, options: [UIViewAnimationOptions(rawValue: UInt(curve))], animations: animateFunc, completion: nil)
}
Then add the target/action methods (called by the observers):
// MARK: - Target/Selector Actions
func keyboardWillShow(notification: NSNotification) {
    if !isKeyboardShowing {
        if let keyboardSize = (notification.userInfo?[UIKeyboardFrameBeginUserInfoKey] as? NSValue)?.cgRectValue {
            let keyboardHeight = keyboardSize.height
            let duration = notification.userInfo?[UIKeyboardAnimationDurationUserInfoKey] as! NSNumber
            let curve = notification.userInfo?[UIKeyboardAnimationCurveUserInfoKey] as! NSNumber
            adjustTableViewInsets(keyboardHeight: keyboardHeight, duration: duration, curve: curve)
        }
    }
}
func keyboardWillHide(notification: NSNotification) {
    let duration = notification.userInfo?[UIKeyboardAnimationDurationUserInfoKey] as! NSNumber
    let curve = notification.userInfo?[UIKeyboardAnimationCurveUserInfoKey] as! NSNumber
    adjustTableViewInsets(keyboardHeight: 0, duration: duration, curve: curve)
}
func keyboardWillChangeFrame(notification: NSNotification) {
    if isKeyboardShowing {
        let duration = notification.userInfo?[UIKeyboardAnimationDurationUserInfoKey] as! NSNumber
        let curve = notification.userInfo?[UIKeyboardAnimationCurveUserInfoKey] as! NSNumber
        if let newKeyboardSize = (notification.userInfo?[UIKeyboardFrameEndUserInfoKey] as? NSValue)?.cgRectValue {
            let keyboardHeight = newKeyboardSize.height
            adjustTableViewInsets(keyboardHeight: keyboardHeight, duration: duration, curve: curve)
        }
    }
}
Lastly, don't forget to remove observers in deinit or in viewWillDisappear:
deinit {
    NotificationCenter.default.removeObserver(self)
}