In view of recent experimental indications of violations of Lepton Flavor Universality (LFU) in B decays, we analyze constraints and implications of LFU interactions, both using an effective theory approach, and an explicit dynamical model. We show that a simple dynamical model based on a SU(2)(L) triplet of massive vector bosons, coupled predominantly to third generation fermions (both quarks and leptons), can significantly improve the description of present data. In particular, the model decreases the tension between data and SM predictions concerning: i) the breaking of tau-mu universality in B --> D-(*())l nu decays; ii) the breaking of mu-e universality in B --> Kl(+)l(-) decays. Indirectly, the model might also decrease the discrepancy between exclusive and inclusive determinations of \V-cb\ and \V-ub\. The minimal version of the model is in tension with ATLAS and CMS direct searches for the new massive vectors (decaying into tau(+)tau(-) pairs), but this tension can be decreased with additional non-standard degrees of freedom. Further predictions of the model both at low- and high-energies, in view of future high-statistics data, are discussed.
