Muon Colliders and Neutrino Factories^*

Over the past decade, there has been significant progress in developing the concepts and technologies needed to produce, capture, and accelerate O(10²¹) muons per year. These developments have paved the way for a new type of neutrino source (neutrino factory) and a new type of very high energy lepton-antilepton collider (muon collider). This article reviews the motivation, design, and research and development for future neutrino factories and muon colliders.