The mechanism responsible for the breaking of the Electroweak Symmetry is the only missing ingredient for the complete theoretical comprehension of Electroweak interactions, unveiling its nature is the main goal of the LHC experimental program. The recent discovery of the Higgs boson, with properties compatible with the predictions of the Standard Model, is the first step in this direction. On one hand, this discovery is a brilliant confirmation of theoretical speculations and of indirect evidences. On the other hand, it leaves a number of open issues which suggest that the Higgs particle might be only the first manifestation of a more rich Electroweak Symmetry Breaking sector, with more new particles to be discovered in the future LHC run. Motivated by the problem of "Naturalness" I will discuss the possibility of the Higgs boson being a composite particle, emerging as a bound state of a new strongly-interacting dynamics, and I will show how this scenario can be discovered or disproved at the LHC. I will argue that searching for "Natural" new physics scenarios, among which Composite Higgs, will change our perspective on the Physics of Fundamental Interactions even with a negative result.