Muon acceleration is one of the most difficult stages to develop for a Neutrino Factory or Muon Collider. The large transverse and longitudinal admittances which must be designed into the system and the rapidity with which acceleration must take place because of muon decay preclude the use of conventional synchrotron design. The current approaches employ fixed-field architectures for muon acceleration: one being a recirculating linac (RLA) with separate fixed-field arcs for each acceleration turn, and another a fixed-field alternating gradient (FFAG) accelerator. Although both scenarios are being actively pursued, this paper emphasizes the FFAG option.