In recent years, there has been a great progress in the development of superparamagnetic particles targeted to a wide range of applications, including fields as diverse as biotechnology or waste removal. However, the physics behind their behaviour under usual conditions (diluted dispersions and high magnetic fields) has many, fundamental, open questions. In this review, we revisit the advances in the basic physical concepts and predictive analytical and simulation tools. We focus on recent developments in the understanding and prediction of phenomena induced by magnetic fields both in uniform fields (for example, chain formation) and in magnetic gradients (cooperative magnetophoresis). © 2013 The Royal Society of Chemistry.