This seminar reviews recent theoretical developments in the study of charged lepton flavour violation. The first part illustrates the status of precise next-to-leading order quantum electrodynamics calculations for the background of charged lepton flavour-violating processes, with a focus on the muonic “rare” and “radiative” decays. Phenomenological implications of these computations and their impact on present and future experiments will be discussed. The second part describes the recent progress in the effective field theory interpretation of charged lepton-flavour violating observables in connection with different energy scales. A systematic approach is briefly presented and applications on muonic and tauonic observables are reported.