Relaxation is a procedure in optimal control problem in which extra elements are added to the domain of an optimization problem in order to guarantee the existence of a minimizer. Of course the relaxed problem, to be of interest, must retain a close relation with the original problem. In this talk, I will give a general survey about the link between relaxation procedure and applications, with a particular attention to examples (and counterexamples). Furthermore I will discuss the case when some pathologies in the relaxation procedure arise and the relation between this phenomenon and the Clarke's Hamiltonian Inclusion.