Searching for Charged Lepton Flavor Violation

Searches for Charged Lepton Flavor Violation (CLFV) are powerful tools to probe physics beyond the Standard Model (BSM). This chapter provides a comprehensive survey of CLFV theory, focusing primarily on low-energy muon and tau transitions while outlining complementary searches from high-energy colliders. Grounded in the Effective Field Theory (EFT) framework, we systematically review key observables including radiative and purely leptonic decays of muon and tau as well as $\mu \to e$ conversion in nuclei and $\tau$ hadronic decay channels. CLFV involving light new physics particles is also discussed. This review captures the modern synergy between EFTs, novel light-mediator scenarios, and hadronic and nuclear physics in the ongoing hunt for BSM signals.