Nanoparticles are finding many applications in medicine and other fields like photonics. Magnetic nanoparticles have additional advantages in medicine over non-magnetic hard nanoparticles, as their magnetic properties make them ideal for hyperthermic applications in therapy and for sensitive diagnostic imaging applications. I review the literature on computational models of the magnetic properties of nanoparticles specifically. Such models have the potential to accelerate the design of magnetic nanoparticles for medical applications. Much of the current literature relates to the modelling of magnetic nanoparticles for inducing hyperthermia in aberrant cells, with significant bodies of work aimed at simulating and predicting properties for medical imaging and targeted delivery of drugs and gene therapies.