ABSTRACT: To solve the quantum measurement problem, models of spontaneous wave function collapse (collapse models) propose to modify
the Schrödinger equation by including nonlinear stochastic terms, describing the collapse of the wave function. These collapses are
“rare” for microscopic systems, their effect adding coherently in composite systems, to the point that  macro-objects are always well
localized. Their dynamics thus differs from the standard quantum one. I will briefly review the main features of collapse models. I will
present an update of the most promising interferometric and non-interferometric tests, showing the current lower and upper bounds
on the collapse parameters. I will also discuss the role that gravity can play in the collapse of the wave function.