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 inthree 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 ofgauge theories on noncommutative spaces, we review our most recent works in which gravity models are constructed as gauge theories on noncommutative spaces.