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. The breakthrough came in 1986, when Ghirardi, Rimini and Weber published the paper with the meaningful title “Unified dynamics for microscopic and macroscopic systems”, where they presented what is now known as the GRW model, after the initials of the authors. The model contains all the ingredients a collapse model should have: The Schrödinger dynamics is modified by adding nonlinear stochastic terms, whose effect is to randomly localize the wave function in space. For microscopic systems, the new terms are mostly negligible. For macroscopic object, the new dynamics keeps the wave function well localized in space, thus ensuring classicality. In particular, at the end of measurements, there are always definite outcomes, distributed according to the Born rule. Deviations from quantum predictions are compatible with current experimental data. In 1990 the efforts for the GRW group on one side, and of P. Pearle on the other side, were brought together in formulating the Continuous Spontaneous Localization (CSL) model, where the Schrödinger dynamics and the random collapse are described within one stochastic differential equation, which is capable of describing also systems of identical particles, a feature which was missing in the GRW model. In the late 1980s and 1990s, Diosi and Penrose independently formulated the idea that the wave function collapse is related to gravity. The dynamical equation is structurally similar to the CSL equation. In the context of collapse models, it is worthwhile to mention the theory of quantum state diffusion. Most popular models Three models are most widely discussed in the literature: Ghirardi–Rimini–Weber (GRW) model: It is assumed that each constituent of a physical system independently undergoes spontaneous collapses. The collapses are random in time, distributed according to a Poisson distribution; they are random in space and are more likely to occur where the wave function is larger. In between collapses, the wave function evolves according to the Schrödinger equation. For composite systems, the collapse on each constituent causes the collapse of the center of mass wave functions. Continuous spontaneous localization (CSL) model: The Schrödinger equation is supplemented with a nonlinear and stochastic diffusion process driven by a suitably chosen universal noise coupled to the mass-density of