Muon colliders, like electron colliders, and in contrast to hadron colliders, offer the potential of physics with well-defined energies and initial states, allowing precision studies at energies up to the center of mass energy of the collider. But because muons are so much heavier than electrons, muons make little synchrotron radiation and can be accelerated and collide in relatively small circular rings, whereas high energy electron colliders must be linear and long.

Muon collider designs will be discussed and compared with those of electron colliders such as the 3-TeV CERN CLIC concept. Significant advantages of muons over electrons are noted.

The state of muon collider R&D will be reviewed and the US decision to end these studies discussed. In view of magnitude of the needed work and the falling level of US HEP funding, the decision, though painful, was not unreasonable.