A review of optimality of multivariate tests

We consider unrestricted (unordered) parametric hypotheses for multivariate or multiparameter distributions and review some optimality aspects, both exact and asymptotic, for testing of hypotheses possibly in the presence of nuisance parameters. The aim is not to provide an exhaustive review but to represent the widely used classical approaches, expose some promising recent ones and present some interesting practical problems requiring the development of new methods.