I will review the parameters and challenges of the proton driven muon colliders using ionization cooling of the muons. I will discuss the experimental studies that have been done, including Merit (on liquid Hg target), MICE (demonstration of ionization cooling), and rf breakdown studies at FNAL with both high pressure gas and beryllium cavities. I will attempt to identify the weakest parts of our current designs. I will also discuss the alternative schemes based on muon production from positron-electron annihilation. I will note that the schemes that I understand, yield disappointingly low luminosities, while those giving good performance seem to violate concepts of phase space conservation. But, then, I may be missing something.