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) as well as lepton flavor violation (LFV). A coherent set of measurements suggests non-standard 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 concrete chances to usher genuinely unexpected discoveries.