The work proposes a methodological solution to complex testing problems. In particular, it is focused on two-sample or multi-sample tests in the presence of multivariate outcomes and very small sample sizes. Parametric solutions are in general very difficult (if not impossible), because there are no degrees of freedom, due to the high number of variables and the low number of observations. Furthermore, the complex (multivariate) nature of the response makes the representation of the dependence structure of the response through a parametric model very difficult and uncertain. Thus, a distribution free approach based on less stringent assumptions about the multivariate underlying distribution but able to capture and implicitly consider the information concerning the dependence between variables, is suitable. The proposed solution belongs to the family of permutation tests. Recent developments, properties and main advantages of this method are presented and discussed in the paper.