The Standard Model (SM) of Particle Physics is currently our best understanding of the laws of nature. At the same time it cannot account for a variety of phenomena, and has a series of shortcomings regarding its own structure.

Beyond the Standard Model physics aims to address these issues, where Grand Unified Theories (GUTs) provide a solution to some of questions regarding the structure, which in turn address some of the phenomenological problems present in the SM.

In the following thesis we explore the phenomenology of GUTs, along with their valid parameter spaces and experimental signatures. This is done within an extra dimensional scenario, where we look at 5D and 6D models, within flat and warped contexts. In this work we have ruled out a series of models and explored the use of unification metrics to guide model building via renormalisation group equation analysis within different regimes. To achieve this we have employed a variety of numerical and evolutionary algorithms.