  In this talk I will review the implications on Standard Model (SM) and Beyond
the SM (BSM) theory of the experimental exploration of the scalar sector. Given
that the Higgs discovery has been the most important achievement, I will start
with a general overview of its dramatic impact on the physics of fundamental
interaction. Next, I will describe how scalar sector results, including the
measurements of the Higgs couplings and mass and the negative searches for
extra scalars, constrain concrete BSM scenarios related with Naturalness. In
particular, I will discuss composite Higgs and low energy supersymmetry, both
in its minimal and next-to-minimal implementations.
