Abstract
Neutrino masses are evidence of lepton flavor violation, but no violation in the interactions among the charged leptons has been observed yet. Many models of Physics Beyond the Standard Model (BSM) predict Charged Lepton Flavor Violation (CLFV) in a wide spectrum of processes with rates in reach of upcoming experiments. The experimental searches that provide the current best limits on the CLFV searches are reviewed, with a particular emphasis on the muon-based experiments that give the most stringent constraints on the BSM parameter space. The next generation of muon-based experiments (MEG-II, Mu2e, COMET, Mu3e) aims to reach improvements by many orders of magnitude with respect to the current best limits, thanks to several technological advancements. We review popular heavy BSM theories, and we present the calculations of the predicted CLFV branching ratios, focusing on the more sensitive sector.