Conceptual design studies are underway for muon colliders and other high-current muon storage rings that have the potential to become the first true ``neutrino factories. Muon decays in long straight sections of the storage rings would produce precisely characterized beams of electron and muon type neutrinos of unprecedented intensity. This article reviews the prospects for these facilities to greatly extend our capabilities for neutrino experiments, largely emphasizing the physics of neutrino interactions.