We briefly overview some theoretical aspects of charged lepton flavour violation in rare muon transitions and decays. Relying on the effective field theory approach (model-independent), we discuss the probing power of charged lepton flavour violation processes regarding the new physics scale, especially in what concerns muon-electron conversion in nuclei. We then illustrate how these processes can provide valuable information (allowing to constrain, falsify - or conversely to learn about the underlying new physics properties) for a few examples of well-motivated extensions of the Standard Model. We finally comment on how leptonic CP violation should be carefully considered upon studies of charged lepton flavour violation in extensions of the Standard Model featuring heavy sterile fermions.