Muon colliders and neutrino factories are attractive options for achieving the highest lepton-antilepton collision energies and the most precise measurements of the parameters of the neutrino mixing matrix. The performance and cost of these future facilities depends sensitively on how well a beam of muons can be cooled. The recent progress of muon-cooling prototype tests and design studies nourishes the hope that such facilities can be built during the next decade.

5 pages, 4 figures, to appear in Proceedings of the XXXIII International Conference on High Energy Physics, Moscow, Russia, July 26 -- August 2, 2006