We examine the prospects for discovering and elucidating the weakly-coupled Higgs sector at future collider experiments. The Higgs search consists of three phases: (i) discovery of a Higgs candidate, (ii) verification of the Higgs interpretation of the signal, and (iii) precision measurements of Higgs sector properties. The discovery of one Higgs boson with Standard Model properties is not sufficient to expose the underlying structure of the electroweak symmetry breaking dynamics. It is critical to search for evidence for a non-minimal Higgs sector and/or new physics associated with electroweak symmetry breaking dynamics. An improvement in precision electroweak data at future colliders can play a useful role in confirming the theoretical interpretation of the Higgs search results.