A central theoretical tension for the semantics of proper names and attitude reports, known as Frege’s puzzle, goes as follows. On the one hand, a simple and attractive theory holds that the sole semantic function of a proper name is to contribute a referent, leading to the prediction that co-referential proper names like Superman and Clark Kent are semantically equivalent.On the other hand, intuition tells us that it could be true to say that Lois Lane believes that Superman is strong while at the same time seemingly false to say that Lois Lane believes that Clark Kent is strong. We survey the three most popular approaches to reconciling this tension: complicating the semantics of proper names (non-rigid designation), complicating the semantics of attitude reports (hidden indexicals), and complicating the pragmatics of attitude reports. We also discuss the related issues of Kripke’s puzzle, as well as Saul’s puzzle concerning substitution of co-referential proper names in simple sentences.