Magnetic separation technology was given new impetus with the introduction of a separator using a matrix of steel wool in a high field combined with an efficient magnetic circuit for the electromagnet. This technology is economically attractive for a wide variety of new separations. The development and status of these applications will be briefly reviewed. This commercial interest stimulated theoretical interest to develop mathematical descriptions of the separation process. The status of the theoretical calculations will be reviewed and their prediction will be compared to the available experimental work. The limitations of the present calculations, and the future directions directions of the modeling work, will be discussed.