Higgs Physics at Future Colliders: recent theoretical developments

I review the physics of the Higgs sector in the Standard Model and its minimal supersymmetric extension, the MSSM. I will discuss the prospects for discovering the Higgs particles at the upgraded Tevatron, at the Large Hadron Collider, and at a future high–energy $e^{+}{e}^{-}$ linear collider with centre–of–mass energy in the 350–800 GeV range, as well as the possibilities for studying their fundamental properties. Some emphasis will be put on the theoretical developments which occurred in the last two years.