Lepton Flavor Violation and Lepton Flavor Universality Violation in b and c Decays

Two topics have recently risen to prominence within the ongoing searches of beyond-Standard Model effects in b and c decays: observables that test lepton flavor universality (LFU) and those that test lepton flavor violation (LFV). A coherent set of measurements suggests nonstandard LFU effects. General arguments relate LFU to LFV, and the observed size of the former gives hope of observable signals for the latter.We attempt a comprehensive discussion of both theoretical and experimental aspects of these tests. The main final message is that all the instruments necessary to fully establish the putative new effects are at hand, thanks to running experiments and their upgrades. Therefore, this subject stands a concrete chance of ushering in genuinely unexpected discoveries.