The search for Higgs bosons is one of the most important motivations for future linear e+e- and photon colliders. In this talk the major aspects of Higgs physics of the Standard Model and its extensions at these two collider types will be reviewed. In particular the measurements of Higgs masses, quantum numbers and couplings via their production and decay processes at a linear e+e- collider will be sortly summarized. Ongoing developments of Higgs boson production via gamma-gamma and tau+ tau- fusion and their impact on coupling and parameter measurements will be discussed in detail.