Leptogenesis provides the most attractive explanation of the matter-antimatter asymmetry of the Universe. It relies on the minimal see-saw mechanism where new very heavy RH neutrinos are added to the SM. The main problem faced by leptogenesis is testability. In my talk I will discuss how imposing the final asymmetry is made independent of the initial conditions ("strong thermal leptogenesis" condition). This favours a lightest neutrino mass greater than about 10 meV, a constraint that will be tested in future years with cosmological observations. I will also discuss a more constrained, SO(10) inspired scenario, where the condition for successful strong thermal leptogenesis leads to quite definite predictions for all the low energy neutrino parameters.