The limit behaviour of variational systems depending on small parameters (e.g. homogenization, phase transitions, etc.) is often successfully described in terms of Gamma-convergence both in the static and quasi-static case as long as a global minimization problem can be formulated. In general, Gamma-convergence is less useful if a local minimization (in the static picture) or gradient flow (in the dynamic case) standpoint is taken. I will recall the (few) known results, and explore some directions of research that take the Gamma-limit as a starting point to obtain "corrected" theories suitable for the description of local minimization or evolutionary problems.