Quantum effects in plasmas are of interest for a diverse set of systems, and have thus as a field been revived and attracted a lot of attention from a wide community over the past decade. In models of quantum plasmas, the effects studied mostly are due to the quantum particle dispersion and tunnelling. Such effects can be of importance in dense systems and on short length scales. There are also a number of effects related to spin and statistics. However, up to recently the magnetization effect in plasmas due to the intrinsic electron spin has been largely ignored. The magnetization dynamics of e.g. solids has many important applications, such as components for memory storage, but has also been discussed in more 'proper' plasma environments, such as fusion plasmas. Furthermore, also from a basic science point-of-view the effects of intrinsic spin and gyromagnetic effects are of considerable interest. Here we give a short review of a number of different models for treating magnetization effects in plasmas, with a focus on recent results. In particular, the transition between kinetic models and fluid models is discussed. We also give a number of examples of applications of such theories, as well as an outlook for possible future work.