Bayesian mixtures are well-established models for density estimation and probabilistic clustering of cross-sectional data. In the last decades, they have also been successfully extended to regression settings. However, there is still currently no consensus on whether and how Bayesian mixture models can handle the analysis of longitudinal data and conduct classification in general frameworks. This work presents some recent advances in longitudinal clustering and classification via Bayesian mixture models, showing novel promising results for the applicability of such models in these settings. The contents of these pages summarize some of the results derived in [12] and [11].