The recent discovery of 2D magnetic order in van der Waals materials has stimulated a renaissance in the field of atomically thin magnets. This has led to promising demonstrations of spintronic functionality such as tunneling magnetoresistance. The frantic pace of this emerging research, however, has also led to some confusion surrounding the underlying phenomena of phase transitions in 2D magnets. In fact, there is a rich history of experimental precedents beginning in the 1960s with quasi-2D bulk magnets and progressing to the 1980s using atomically thin sheets of elemental metals. This review provides a holistic discussion of the current state of knowledge on the three distinct families of low-dimensional magnets: quasi-2D, ultrathin films, and van der Waals crystals. It highlights the unique opportunities presented by the latest implementation in van der Waals materials. By revisiting the fundamental insights from the field of low-dimensional magnetism, this review highlights factors that can be used to enhance material performance. For example, the limits imposed on the critical temperature by the Mermin–Wagner theorem can be escaped in three separate ways: magnetocrystalline anisotropy, long-range interactions, and shape anisotropy. Several recent experimental reports of atomically thin magnets with Curie temperatures above room temperature are highlighted.