Higgs Phenomenology with CPsuperH

The MSSM contains CP-violating phases that may have important observable effects in Higgs physics. We review recent highlights in Higgs phenomenology obtained with the code CPsuperH, a useful tool for studies of the production, mixing and decay of a coupled system of the neutral Higgs bosons at future high energy colliders such as the LHC, ILC ($\gamma$LC), and a muon collider (MC). CPsuperH implements the constraints from upper limits on electric dipole moments, and may be extended to include other related low-energy observables, such as b -> s \gamma and B -> K l l, and to compute the relic abundance of the lightest neutralino