I am trying to check when a text field changes, equivalent too the function used for textView - textViewDidChange so far I have done this: 
  fu         
        Swift 4
Conform to UITextFieldDelegate.
func textField(_ textField: UITextField, shouldChangeCharactersIn range: NSRange, replacementString string: String) -> Bool {
    // figure out what the new string will be after the pending edit
    let updatedString = (textField.text as NSString?)?.replacingCharacters(in: range, with: string)
    // Do whatever you want here
    // Return true so that the change happens
    return true
}
There's now a UITextField delegate method available on iOS13+
optional func textFieldDidChangeSelection(_ textField: UITextField)
Just in case you are interested in a SwiftUI solution, this it's working for me:
 TextField("write your answer here...",
            text: Binding(
                     get: {
                        return self.query
                       },
                     set: { (newValue) in
                        self.fetch(query: newValue) // any action you need
                                return self.query = newValue
                      }
            )
  )
I have to say it's not my idea, I read it in this blog: SwiftUI binding: A very simple trick
Swift 3.0.1+ (Some of the other swift 3.0 answers are not up to date)
textField.addTarget(self, action: #selector(ViewController.textFieldDidChange(_:)),
                          for: UIControlEvents.editingChanged)
func textFieldDidChange(_ textField: UITextField) {
}
In case it is not possible to bind the addTarget to your UITextField, I advise you to bind one of them as suggested above, and insert the code for execution at the end of the shouldChangeCharactersIn method.
nameTextField.addTarget(self, action: #selector(RegistrationViewController.textFieldDidChange(_:)), for: .editingChanged)
@objc func textFieldDidChange(_ textField: UITextField) {
    if phoneNumberTextField.text!.count == 17 && nameTextField.text!.count > 0 {
        continueButtonOutlet.backgroundColor = UIColor(.green)
    } else {
        continueButtonOutlet.backgroundColor = .systemGray
    }
}
And in call in shouldChangeCharactersIn func.
func textField(_ textField: UITextField, shouldChangeCharactersIn range: NSRange, replacementString string: String) -> Bool {
    guard let text = textField.text else {
        return true
    }
    let lastText = (text as NSString).replacingCharacters(in: range, with: string) as String
    if phoneNumberTextField == textField {
        textField.text = lastText.format("+7(NNN)-NNN-NN-NN", oldString: text)
        textFieldDidChange(phoneNumberTextField)
        return false
    }
    return true
}
You can make this connection in interface builder.
In your storyboard, click the assistant editor at the top of the screen (two circles in the middle).
Ctrl + Click on the textfield in interface builder.
Drag from EditingChanged to inside your view controller class in the assistant view.
Name your function ("textDidChange" for example) and click connect.