  It has been known for some time that warped extra dimensions offer a
potential explanation of the large hierarchy that exists between the
electroweak scale and the Planck scale. The majority of this work has focused
on a five dimensional slice of AdS space. This thesis attempts to address the
question, what possible spaces offer phenomenologically viable resolutions to
this gauge hierarchy problem. In order for a space to offer a potential
resolution to the hierarchy problem two conditions must be met: Firstly one
should be able to demonstrate that the space can be stabilised such that a
small effective electroweak scale (or large effective Planck scale) can be
obtained. Secondly one must demonstrate that the space allows for a Kaluza
Klein (KK) scale that is small enough such that one does not reintroduce a
hierarchy in the effective theory. Here we focus on the second condition and
examine the constraints, on the KK scale, coming from corrections to
electroweak observables and flavour physics which arise when gauge fields
propagate in an additional dimension. We study a large class of possible spaces
of different geometries and dimensionalities. In five dimensions it is found
that such constraints are generically large. In more than five dimensions it is
found that a significant proportion of such spaces suffer from either a high
density of KK modes or alternatively strongly coupled KK fields. The latter
would not offer viable resolutions to the hierarchy problem. Models in which
the Higgs propagates in the bulk are also studied, in the context of models
with a `soft wall' and it is found these have significantly reduced constraints
from flavour physics as well as a notion of a minimum fermion mass.
