The interface of quantum mechanics and gravity is among the most interesting topics in theoretical as well as experimental physics. On the theoretical side, we are forced to address how to model quantum systems in situations where gravity is no longer negligible but rather provides the main lever for modifying genuine quantum phenomena. On the experimental side, we are confronted by the unique challenge of devising schemes capable of detecting subtle gravitational effects on quantum systems. The strict theoretical consistency constraints and the experimental realities have pushed physicists to scrutinize how the notions of space and time, as well as the gravitational field, connect to the world of quantum probabilities.
We will start by reviewing some key concepts of general relativity, placing non-inertial and gravitational phenomena accessible in the laboratory in the context of the spacetime metric. Using a minimal description based on effective quantum Hamiltonians in the weak-field regime, alongside a general relativistic interpretation, we will review selected experimental milestones, including the Colella-Overhauser-Werner experiment, Sagnac interferometry, spacetime curvature measurements and the observation of the gravitational Aharonov-Bohm effect. We will then discuss emerging experimental proposals in which gravity is either actively controlling or generating quantum phenomena. We will consider both quantum probes of gravitational fields and quantum sources of gravity, revisiting key concepts related to gravitationally induced entanglement and decoherence. In the final part, we will classify different theoretical approaches according to their treatment of the gravitational field and its coupling to quantum matter, highlighting their observable consequences and the theoretical questions they raise.