  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.
