Abstract: Open systems with gain and loss, described by non-Hermitian Hamiltonians, have been a subject of intense research recently. In classical optical systems, the effect of exceptional-point degeneracies on their dynamics has been observed through remarkable phenomena such as the parity-time (PT) symmetry breaking transition, asymmetric mode switching, and optimal energy transfer. After a brief history of the field of PT symmetry, started by Carl Bender and co-workers, I will discuss quantum realizations of such systems with single photons, ultracold atoms, and superconducting transmon circuits. Results include observation of PT transitions at vanishingly small non-Hermiticity in the Floquet domain, information flow in a PT-symmetric system, and a quantum signature of the exceptional point in the qubit relaxation state. I will argue that non-Hermiticity provides a new dimension for exploring quantum systems.