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In this survey, our aim is to emphasize the main known limitations to the useof Wigner measures for Schrodinger equations. After a short review ofsuccessful applications of Wigner measures to study the semi-classical limit ofsolutions to Schrodinger equations, we list some examples where Wigner measurescannot be a good tool to describe high frequency limits. Typically, the Wignermeasures may not capture effects which are not negligible at the pointwiselevel, or the propagation of Wigner measures may be an ill-posed problem. Inthe latter situation, two families of functions may have the same Wignermeasures at some initial time, but different Wigner measures for a larger time.In the case of systems, this difficulty can partially be avoided by consideringmore refined Wigner measures such as two-scale Wigner measures; however, wegive examples of situations where this quadratic approach fails.

On the time evolution of Wigner measures for Schrodinger equations