The measurement problem casts serious doubts on quantum mechanics as a universal theory of Nature, since the linearity of the Schroedinger equation is in conflict with our everyday experience. Several solutions to this problem have been proposed. I will discuss on one such solution: models of spontaneous wave function collapse. I will describe their general properties. I will discuss the lower and upper bounds on the collapse parameters. I will review their status as phenomenological modifications of quantum mechanics, whose predictions can be tested experimentally.