We discuss possible acceleration scenarios and methods for a mu+ mu- collider. The accelerator must take the beams from ~100 MeV to 2 TeV within the muon lifetime (2.2 x 10**(-6) E(mu)/m(mu) uS), while compressing bunches of 10**(12) muons from m to cm bunch lengths. Linac, recirculating linac, and very rapid-cycling synchrotron approaches are studied. Multiple recirculating linac approaches are matched to the muon lifetime and appear readily feasible. Rapid-cycling approaches require innovations in magnet designs and layouts, but could be much more affordable.