The relationship between the strength of lepton flavour violating processes and the magnitude of the neutrino mass is rather model dependent. I review this question within different neutrino mixing models including superstring inspired models. Processes such as μ → e + γ, μ → 3 e, μ- e conversion in nuclei, etc. as well as lepton flavour violating Z° decays can occur even if the physical neutrinos are strictly massless. As a result, the corresponding rates are unconstrained by bounds on the neutrino mass that follow from laboratory, astrophysics and cosmology and can therefore be large. Leptonic CP violation may also occur even when the physical neutrinos are strictly massless.