The Standard Model of fundamental interactions, albeit an incredibly elegant and successful theory, lacks explanations for some experimental and theoretical open questions. Interestingly, many of these problems seem to be related to the electroweak symmetry breaking sector of the theory, whose dynamical generation is still unknown. Important questions such as what is the true nature of the Higgs boson, why is its mass so light and so close to that of the electroweak gauge bosons or whether the properties of this particle are the ones predicted in the Standard Model remain unanswered. The LHC is our tool to unveil these mysteries and vector boson scattering processes are the perfect window to access them, since they are considered as the most sensitive observables to new physics in the electroweak symmetry breaking sector. In this Thesis we employ the effective electroweak chiral Lagrangian with a light Higgs, which assumes a strongly interacting electroweak symmetry breaking sector, to perform a model independent analysis of the phenomenology of vector boson scattering processes at the LHC as well as to present quantitative predictions for the sensitivity to possible beyond the Standard Model physics scenarios.