 Two specifications are necessary in order to make clear from the beginning what the limitations and the merits of the program are. The only satisfactory explicit models of this type (the model proposed by Ghirardi, Rimini, and Weber (1986), usually referred to as the GRW theory, as well as all subsequent developments) are phenomenological attempts to solve a foundational problem. At present, they involve phenomenological parameters which, if the theory is taken seriously, acquire the status of new constants of nature. Moreover, the problem of building satisfactory relativistic generalizations of collapse models is very difficult, though some improvements have been made, which have elucidated some crucial points. 