Abstract: "In this talk, we discuss a new kind of symmetry that underlies a wide class of driven-dissipative quantum systems, a *hidden time-reversal symmetry*. This symmetry represents a generalization of the notion of “detailed balance” that is fully applicable to truly quantum systems. The introduction of this symmetry resolves the problem of how to usefully define “detailed balance” in a quantum setting (a problem that has been studied since the early 70’s by AMO physicists). This symmetry also resolves the open problem of why certain nonlinear driven-dissipative quantum problems have exact solutions, for example a class of driven nonlinear resonator problems first solved in the 80’s by Drummond using the complex-P function technique. Our work shows these exact solutions arise because of a quantum time-reversal symmetry that can exist in systems that are truly many-body in nature – even systems which at first glance seem totally unrelated, e.g. driven-dissipative spin chains. We prove a theorem that establishes a direct relationship between these symmetries in a wide class of driven-dissipative systems. In the final part of our talk, we show how this symmetry has been used recently to discover exact solutions of a new class of many-body driven-dissipative systems. As highlights, we investigate dissipative, liquid-gas type transitions in the fully-connected transverse-field Ising model with local longitudinal ($T_1$) qubit relaxation, as well as a kind of dissipative, two-photon-driven global Hubbard model that can be defined on a lattice in arbitrary spatial dimensions. Both of these models were not previously known to be exactly solvable, and represent hopefully a new class of toy models where questions about phase transitions and critical phenomena in a fully-quantum and nonequilibrium setting can be studied without making any approximations."