  First, we briefly review the Coset Space Dimensional Reduction scheme and the
results of the best model so far. Then, we present the introduction of fuzzy
coset spaces used as extra dimensions and perform a dimensional reduction. In
turn, we describe a construction which mimics the results of a reduction,
starting from a 4-dimensional theory and we present a successful example of a
dynamical generation of fuzzy spheres. Finally, we propose a construction of
the 3-d gravity as a gauge theory on specific non-commutative spaces.
