Quantum mechanics is a cornerstone of modern physics and at the very basis of the Standard
Model. However, decades-old open questions at its foundations, such as the "measurement
problem" and the wave function collapse are still with us. Moreover, theories beyond the Standard
Model often include extra-dimensions and violation of the Lorentz/Poincaré symmetries which
could entail a departure from the predictions of the standard quantum mechanics. At the Gran
Sasso underground laboratory in Italy, we search for small, beyond the quantum theory signals
using radiation detectors. In particular, emission of spontaneous radiation is predicted by gravity-
related and continuous spontaneous localization (CSL) collapse models. We have ruled out the
natural parameter-free version of the Diósi-Penrose (DP) model, and put stringent limits on the
CSL model. In addition, with the VIP-2 experiment we are searching for possible violations of
the Pauli Exclusion Principle (PEP) in forbidden atomic transitions. The impact of this research
on quantum gravity models, as well as its experimental upgrade VIP-3 is also discussed.