Is there a built-in way to get from a UIView to its UIViewController? I know you can get from UIViewController to its UIView
There is no way.
What I do is pass the UIViewController pointer to the UIView (or an appropriate inheritance). I'm sorry I can't help with the IB approach to the problem because I don't believe in IB.
To answer the first commenter: sometimes you do need to know who called you because it determines what you can do. For example with a database you might have read access only or read/write ...