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.
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