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This note reviews recent theoretical developments in the study of chargedlepton flavour violation. The first part illustrates the status of precisenext-to-leading order quantum electrodynamics calculations for the backgroundof charged lepton flavour-violating processes, with a focus on the muonic"rare" and "radiative" decays. Phenomenological implications of thesecomputations and their impact on present and future experiments will bediscussed. The second part describes the recent progress in the effective fieldtheory interpretation of charged lepton-flavour violating observables inconnection with different energy scales. A systematic approach is brieflypresented and applications on muonic and tauonic observables are reported. Thisnote is submitted as part of the conference proceedings for "NuPhys2016:Prospects in Neutrino Physics".

Charged lepton flavour violation: precise background calculation and effective field theoretical interpretation