[en] Conceptual design studies are underway for both muon colliders and high-current non-colliding 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 uniquely intense and precisely characterized two-component neutrino beams--muon neutrinos plus electron antineutrinos from negative muon decays and electron neutrinos plus muon antineutrinos from positive muons. This article presents a long-term overview of the prospects for these facilities to greatly extend the capabilities for accelerator-based neutrino physics studies for both high rate and long baseline neutrino experiments. As the first major physics topic, recent experimental results involving neutrino oscillations have motivated a vigorous design effort towards dedicated neutrino factories that would store muon beams of energies 50 GeV or below. These facilities hold the promise of neutrino oscillation experiments with baselines up to intercontinental distances and utilizing well understood beams that contain, for the first time, a substantial component of multi-GeV electron-flavored neutrinos. In deference to the active and fast-moving nature of neutrino oscillation studies, the discussion of long baseline physics at neutrino factories has been limited to a concise general overview of the relevant theory, detector technologies, beam properties, experimental goals and potential physics capabilities. The remainder of the article is devoted to the complementary high rate neutrino experiments that would study neutrino-nucleon and neutrino-electron scattering and would be performed at high performance detectors placed as close as is practical to the neutrino production straight section of muon storage rings in order to exploit beams with transverse dimensions as small as a few tens of centimeters