  The prospects are explored for testing Lorentz and CPT symmetry in the muon
sector via the spectroscopy of muonium and various muonic atoms, and via
measurements of the anomalous magnetic moments of the muon and antimuon. The
effects of Lorentz-violating operators of both renormalizable and
nonrenormalizable dimensions are included. We derive observable signals,
extract first constraints from existing data on a variety of coefficients for
Lorentz and CPT violation, and estimate sensitivities attainable in forthcoming
experiments. The potential of Lorentz violation to resolve the proton radius
puzzle and the muon anomaly discrepancy is discussed.
