In recent years, the (string-inspired) paradigm of modular invariance has been applied to the SM flavour puzzle with interesting results. Taking a bottom-up approach, one relies on very simple scalar sectors. Indeed, couplings and mass matrices can be functions of a single complex VEV, which is the only source of flavour symmetry breaking and of CP violation. Such setups can be used to predict neutrino masses, neutrino mixing angles and all (Dirac and Majorana) CP violating phases in the lepton sector. They may also shed light on the origin of fermion mass hierarchies.