The traditional view from particle physics is that quantum-gravity effects should become detectable only at extremely high energies and small length scales. Owing to the significant technological challenges involved, there has been limited progress in identifying experimentally detectable effects that can be accessed in the foreseeable future. However, in recent decades the size and mass of quantum systems that can be controlled in the laboratory have reached unprecedented scales, enabled by advances in ground-state cooling and quantum-control techniques. Preparations of massive systems in quantum states pave the way for the explorations of a low-energy regime in which gravity can be both sourced and probed by quantum systems. Such approaches constitute an increasingly viable alternative to accelerator-based, laser-interferometric, torsion-balance, and cosmological tests of gravity. In this review an overview of proposals where massive quantum systems act as interfaces between quantum mechanics and gravity is provided. Conceptual difficulties in the theoretical description of quantum systems in the presence of gravity are discussed, tools for modeling massive quantum systems in the laboratory are reviewed, and an overview of the current state-of-the-art experimental landscape is provided. Proposals covered in this review include precision tests of gravity, tests of gravitationally induced wave-function collapse and decoherence, and gravity-mediated entanglement. The review concludes with an outlook and summary of the key questions raised.