I will define a notion of resolution of a proper action. Such resolutions always exist but are not canonical. However, for so-called polar actions I will describe a canonical construction of a resolution, which can be used to show that the leaf space has the structure of an orbifold. I will illustrate this construction with two examples: (i) the adjoint action, where it allows one to identify the classical Weyl group with the orbifold fundamental group; and (ii) toric manifolds, where the resolution can be described in terms of the real part of the toric manifold.