  One of the main motivations for low energy supersymmetric theories is their
ability to address the hierarchy and naturalness problems in the Higgs sector
of the Standard Model. In these theories, at least two doublets of scalar
fields are required to break the electroweak symmetry and to generate the
masses of the elementary particles, resulting in a rather rich Higgs spectrum.
The search for the Higgs bosons of Supersymmetry and the determination of their
basic properties is one of the major goals of high--energy colliders and, in
particular, the LHC which will soon start operation. We review the salient
features of the Higgs sector of the Minimal Supersymmetric Standard Model and
of some of its extensions and summarize the prospects for probing them at the
LHC and at the future ILC.
