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.
