Quantum mechanics and general relativity provide extraordinarily successful yet conceptually incompatible descriptions of nature. Levitated mechanical systems offer a new route to testing their interface: they combine comparatively large masses with exceptional isolation, precision control and force sensitivity. We will present our recent progress towards experiments probing quantum mechanics and gravity with massive systems. On the tabletop, this includes the detection of attonewton-scale gravitational forces using a milligram-scale particle magnetically levitated above a superconductor, alongside proposals and techniques for testing gravitational decoherence, collapse models and whether gravity can act as a quantum mediator. We will then discuss how nanoparticle interferometry could create spatial quantum superpositions approaching or exceeding the dimensions of the particle itself. Finally, we will describe why space provides a uniquely favourable environment for such experiments, enabling long free-evolution times and reduced terrestrial disturbances, and present our development and flight of a compact levitated-mechanics platform. Together, these advances outline a path from precision measurements on the laboratory bench towards decisive tests of quantum mechanics and gravity in space.