In the proposed project, various aspects of the phenomenology of physics Beyond the Standard Model (BSM) will be analyzed, aiming to an improvement in our understanding of what might complete the SM at high energies.After the first run of the LHC, with the discovery of a Higgs boson, valuable new information about possible extensions of the SM is available. Thus, a first emphasis of the project is put on Higgs physics. A comprehensive survey of Higgs production and decay in classes of Gauge-Higgs Unification models will be presented and interpreted in the light of the experimental results, taking into account effects from resonances and fermion mixings that have been usually neglected so far. Both options of embedding the SM fermions into fundamental and adjoint representations of SO(5) will be considered. A focus will be on effects from a realistic lepton sector, realized with the help of an A4 symmetry, that leads to interesting effects in Higgs physics due to a rather composite $\tau$ lepton.Moreover, a model-independent analysis of possible new physics effects in Higgs-pair production will be provided, taking in particular into account constraints from single Higgs production. This analysis will lead to additional valuable information about the Higgs sector.Beyond that, the flavor sector of less restricted 4D realizations of the Pseudo-Goldstone Higgs setup will be studied, considering all possible constraints and in particular new results from the LHCb experiment. These will also be interpreted in the general BSM context. Concerning lepton flavor, the room for having a composite $\tau$, as considered before, will be analyzed in detail.In the more conceptual part, an alternative approach to the hierarchy problem, assuming new physics at larger scales, will be entertained. Finally, possible interesting implications of see-saw models for LHC or linear-collider physics will be analyzed.