The physical principles underlying some current biomedical applications of magnetic nanoparticles are reviewed. Starting from well-known basic concepts, and drawing on examples from biology and biomedicine, the relevant physics of magnetic materials and their responses to applied magnetic fields are surveyed. The way these properties are controlled and used is illustrated with reference to (i) magnetic separation of labelled cells and other biological entities; (ii) therapeutic drug, gene and radionuclide delivery; (iii) radio frequency methods for the catabolism of tumours via hyperthermia; and (iv) contrast enhancement agents for magnetic resonance imaging applications. Future prospects are also discussed.