In this paper, we review some mathematical models describing drug release from affinity-based drug delivery systems. We discuss various classes of affinity-based systems that have been developed for drug delivery, and highlight some of the practical difficulties associated with developing systems to achieve desired release profiles. We consider the role mathematical modelling can play in assisting with the design of these systems, and illustrate how the models may be analyzed using analytical and numerical techniques. Mathematical modelling can yield valuable insights into the underlying release mechanisms and can streamline the development process by informing the design of experiments. It is shown that the models are capable of reproducing many of the key features of the release profiles observed in in-vitro release experiments.