Thermomagnetic recording is the production of a remanent magnetization in a material by cooling it from a critical temperature in a small magnetic field. The most prominent applications for thermomagnetic recording presently under consideration are high density information storage and tape copying; other applications, e.g., display and magnetic printing, can also be envisioned. In this review of the field, we discuss the proposed applications of thermomagnetic recording, the physical principles of the various magnetic phenomena that can be used for this purpose, and the degree to which specific materials meet the requirements for thermomagnetic recording.