The recent progress in direct active cooling of the quantum-electric degrees of freedom in engineered circuits, or quantum-circuit refrigeration is reviewed. In 2017, the discovery of a quantum-circuit refrigerator (QCR) based on photon-assisted tunneling of quasiparticles through normal-metal–insulator–superconductor junctions inspired a series of experimental studies demonstrating the following main properties: i) the direct-current (dc) bias voltage of the junction can change the QCR-induced damping rate of a superconducting microwave resonator by orders of magnitude and give rise to nontrivial Lamb shifts, ii) the damping rate can be controlled in nanosecond time scales, and ii) the dc bias can be replaced by a microwave excitation, the...