 As stressed in the opening sentences of this contribution, the most serious problem of standard quantum mechanics lies in its being extremely successful in telling us about what we observe, but being basically silent on what there is. This specific feature is closely related to the probabilistic interpretation of the statevector, combined with the completeness assumption of the theory. Notice that what is under discussion is the probabilistic interpretation, not the probabilistic character, of the theory. Also collapse theories have a fundamentally stochastic character but, due to their most specific feature, i.e., that of driving the statevector of any individual physical system into appropriate and physically meaningful manifolds, they allow for a different interpretation. One could even say (if one wants to avoid that they too, as the standard theory, speak only of what we find) that they require a different interpretation, one that accounts for our perceptions at the appropriate, i.e., macroscopic, level.