Adiabatic demagnetization refrigerators (ADR), based on the magnetocaloric effect, are solid--state coolers that were the first to achieve cooling well into the sub--kelvin regime. Although supplanted by more powerful dilution refrigerators in the 1960s, ADRs have experienced a revival due to the needs of the space community for cooling astronomical instruments and detectors to temperatures below 100 mK. The earliest of these were single--stage refrigerators using superfluid helium as a heat sink. Their modest cooling power (<1 µW at 60 mK[1]) was sufficient for the small (6x6) detector arrays[2], but recent advances in arraying and multiplexing technologies[3] are generating a need for higher cooling power (5--10 µW), and lower temperature (<30 mK). Single--stage ADRs have both practical and fundamental limits to their operating range, as mass grows very rapidly as the operating range is expanded. This has led to the development of new architectures that introduce multi--staging as a way to improve operating range, efficiency and cooling power. Multi--staging also enables ADRs to be configured for continuous operation, which greatly improves cooling power per unit mass. This paper reviews the current field of adiabatic demagnetization refrigeration, beginning with a description of the magnetocaloric effect and its application in single--stage systems, and then describing the challenges and capabilities of multi--stage and continuous ADRs.