Aspects of extra dimensional supersymmetric unified theories

The purpose of this work is to investigate Grand Unified Theories (GUTs) and to make the link with passed and upcoming experiments. The structure of this thesis is as follows. In the first chapter, we will briefly review the sequence of arguments leading to the Higgs mechanism, then to the different concepts underlying physics beyond the Standard Model, and to the paradigm of extra dimensional supersymmetric grand unified theories. At each level of the argumentation, we will mention the different solutions available. The second chapter introduces more formally supersymmetry and extra dimensions, focusing in particular on the aspects of symmetry breaking. Then, in the third chapter, we present in details the two frameworks of extra dimensional theories in which we worked, called supersymmetric gauge-Higgs unification (GHU) and holographic grand unification (HGU) as well as the developments and modifications we brought to them. The fourth chapter is devoted to the low energy viability of the GHU framework, as well as its phenomenological implications. The fifth chapter presents a more generic study of the property of GUT-scale degenerate Higgs mass matrix, common to both frameworks. Finally, the sixth chapter is devoted to the viability and phenomenological implications of the HGU framework, with special emphasis on lepton flavour violation. This quantitative study takes properly into account effects of matrix anarchy, as well as exact flavour observables. The results obtained should generalize, at least qualitatively, to any other model with similar localization and supersymmetry breaking features