We use an effective Lagrangian approach to address the question of the dynamics of electroweak symmetry breaking in the Standard Model (SM) and its relation to the hierarchy problem. Composite Higgs models provide a solution by describing the recently discovered Higgs-like scalar particle as a composite pseudo Nambu-Goldstone boson that dissolves into its constituents above a certain high energy scale. We discuss many features of the low energy description of composite Higgs models and present an explicit realisation in a flat extra dimension showing explicitly that top partners with masses below 1TeV are expected in a natural theory. Naturalness requires New Physics not much above the weak scale and hence motivates the search for direct and indirect evidence of physics beyond the SM at the LHC and future colliders. As an indirect probe at the LHC, we propose a dedicated analysis of single top production in association with a Higgs boson to lift the degeneracy in the sign of the top Yukawa coupling. We move on to an extensive study of WW scattering, double and triple Higgs production at future linear colliders to estimate their impact on the parameter space of a strongly interacting Higgs boson. Direct probes of New Physics at the LHC include the search for heavy vectors and fermions. We introduce a model-independent strategy to study narrow resonances which we apply to a heavy vector triplet of the SM for illustration. We conclude by summarising current constraints and the expected reach of future colliders on the parameter space of a minimal composite Higgs model. This thesis is based on the papers in Refs. [1–4].