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 MSS M. 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. (author)