We review evolutionary models for the progenitor of SN 1987A and contront these models with available observational/theoretical constraints. For this purpose, we devise five tests a successful model has to fulfill. These include the three major anomalies of the supernova (the blue color of the progenitor, the ring surrounding it and the progenitor's chemical anomalies), the characteristics of the supernova explosion, and general consistency with the theory of massive stars. We show that single-star models (with teh possible exception of rapid-rotation models) fail at least two of these tests, while two binary models (accretion and merger models) are consistent with all available constraints. We conclude that it is most likely that the progenitor of SN 1987A had a binary companion, either at the time of the explosion or at least in the not-too-distant past. We discuss in detail how future observations and theoretical calculations are likely to settle this issue conclusively.