  First, we briefly review the description of gravity theories as gauge
theories in three and four dimensions. Specifically, we recall the procedure in
which the results of General Relativity in three and four dimensions are
recovered in a gauge-theoretic approach. Also, the procedure is applied for the
case of the Weyl gravity, too. Then, after reminding briefly the formulation of
gauge theories on noncommutative spaces, we review our most recent works in
which gravity models are constructed as gauge theories on noncommutative
spaces.
