The following pages contain a review of some recent and ongoing work on model-based clustering, in particular hard and soft assignment. It is analysed up to which point, with modern tools of optimization and parallel computing, it is possible to use basic methods such as maximum likelihood and hard assignment towards automatic identification of the classes and of the class labels of the sampled subjects. The standard soft classification approach using the EM (expectation maximization) algorithm will be compared to the hard assignment approach using maximum likelihood. The latter's limits will be analysed at a computational level, under and without the presence of hypotheses of local independence. Limits and applications of such algorithms to real datasets will be shown.