Polymer core–shell nanoparticles are attractive drug-delivery systems because the drug can be encapsulated inside the core, while the shell properties can be assigned to optimise drug-delivery needs. An elegant approach to such particles is to use polymer gels, which have swelling properties that depend upon conditions such as pH. In this way swelling of the shell, and the drug release, can be targeted to occur at the desired location. We use computer simulations to capture the deformation of polymer core–shell nanoparticles and, subsequently, the drug diffusion from the core of these structures. In particular, we investigate the effects of shell swelling on drug-release rates, where the expanding shell leaves more free space for the drug to diffuse out of the core. Furthermore, we introduce enthalpic interactions and investigate both the physical and chemical barriers to drug release. Therefore, through a combination of structural and fluid simulations we can capture the physics of polymer core–shell nanoparticles and their uses for drug delivery.