Abstract: Massive neutrinos and leptonic mixing have provided the first evidence of flavour violation in the lepton sector, opening a unique gateway to many new phenomena, with an impact ranging from low-energy observables to colliders, as well as cosmology and astroparticle physics. If observed, charged lepton flavour violation (cLFV) is a clear sign of New Physics - beyond the Standard Mode (SM) minimally extended to accommodate neutrino oscillation data. After a brief review of the experimental status of cLFV searches, both at low- and high-energies, we comment on the prospects for the upcoming years. We then consider extensions of the SM which could potentially give rise to observable cLFV signals.