Partial group actions on spaces by homeomorphisms between open sets provide a rich class of C*-algebras via the crossed product construction. We start an in-depth investigation when a general Hausdorff étale groupoid is a transformation groupoid by a partial action. Our negative results contain the first examples of Hausdorff étale groupoids which do not arise as transformation groupoids of partial group actions and which are not inner amenable in the sense of Anantharaman-Delaroche. On the positive side, we prove that many higher rank graph algebras as well as many unital UCT Kirchberg algebras can be realized via partial group actions. This is joint work with Alcides Buss.