Abstract: We consider an extreme type-II superconducting wire with non-smooth cross section, i.e., with one or more corners at the boundary, in the framework of the Ginzburg-Landau theory. We prove the existence of an interval of values of the applied field, where superconductivity is spread uniformly along the boundary of the sample. More precisely the energy is not affected to leading order by the presence of corners and the modulus of the Ginzburg-Landau minimizer is approximately constant along the transversal direction. The critical fields delimiting this surface superconductivity regime coincide with the ones in absence of boundary singularities. We will also discuss some recent results. In particular, we introduce a new effective problem near the corner that allows us to prove a refined asymptotics and to isolate the contributions to the energy density due to the presence of corners. The explicit expression of the effective energy is yet to be found but we formulate a conjecture on it based on the behavior for almost flat angles. Indeed, for corners with angles close to ππ, we are able to explicitly compute the leading order of the corners effective problem and show that it sums up to the smooth boundary contribution to reconstruct the same asymptotics as in smooth domains. Joint work with Michele Correggi.