The genesis of collapse models dates back to the 1970s. In Italy, the group of L. Fonda, G.C. Ghirardi and A. Rimini was studying how to derive the exponential decay law in decay processes, within quantum theory. In their model, an essential feature was that, during the decay, particles undergo spontaneous collapses in space, an idea that was later carried over to characterize the GRW model. Meanwhile, P. Pearle in the USA was developing nonlinear and stochastic equations, to model the collapse of the wave function in a dynamical way; this formalism was later used for the CSL model. However, these models lacked the character of “universality” of the dynamics, i.e. its applicability to an arbitrary physical system (at least at the non-relativistic level), a necessary condition for any model to become a viable option.