  Theories defined in higher than four dimensions have been used in various
frameworks and have a long and interesting history. Here we review certain
attempts, developed over the last years, towards the construction of unified
particle physics models in the context of higher-dimensional gauge theories
with non-commutative extra dimensions. These ideas have been developed in two
complementary ways, namely (i) starting with a higher-dimensional gauge theory
and dimensionally reducing it to four dimensions over fuzzy internal spaces and
(ii) starting with a four-dimensional, renormalizable gauge theory and
dynamically generating fuzzy extra dimensions. We describe the above approaches
and moreover we discuss the inclusion of fermions and the construction of
realistic chiral theories in this context.
