In this thesis I propose a model, and associated algorithms, for on-line community detection in dynamic networks. I test the performance of the algorithms on synthetic networks generated by the Dynamic Stochastic Block model, focusing on the question whether we can, at every moment in the network's dynamics, infer its organization in communities and learn the unknown parameters that were used to generate it, based on the only knowledge of the connections between pairs of nodes. We extend the analysis studied in literature on the phase diagrams of Belief Propagation algorithms for community detection, using the cavity method of statistical physics to evaluate the phase diagram of our and existing models.