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The discovery of the Higgs was a milestone in particle physics and measurements of its properties are long range priorities of the community.   While precise measurements of Higgs properties point agree with the prediction of the Standard Model of Particle Physics, there is still much to learn.  In this talk, I will focus on what searches at the LHC and future collides can help shed light the Higgs sector, and what we may still be missing.  In particular, simple, but concrete, scalar extensions of the Standard Model Higgs can help explain some fundamental problems in particle physics and provide many new search channels at colliders.