White dwarf binaries, like cataclysmic variables (CV), AM CVn systems and extremely low-mass white dwarfs, are among the most abundant compact objects in the Galaxy, yet both their population across stellar environments and the physical mechanisms driving their outbursts remain poorly constrained. Using TESS, I will show how systematic outburst surveys of AM CVn systems place new constraints on disc instability models. I will then present results from a search for variable compact objects in globular clusters using archival HST data, motivated by the long-standing discrepancy between the predicted and observed CV population in these environments. Results include the discovery of several candidate magnetic extremely low-mass white dwarfs in NGC 6397 and the measurement of the orbital period of a redback millisecond pulsar. Double white dwarf binaries are also prime targets for future gravitational wave (GW) detectors; the last part of the talk will focus on multi-messenger studies of these systems, discussing how proposed lunar GW observatories could detect their mergers at extragalactic distances with weeks of advance warning, enabling a new era of coordinated electromagnetic follow-up.
