Stimuli-sensitive hydrogels are an exciting class of materials with widespread potential for use in engineering and biomedical applications. The design of advanced functional devices using hydrogels requires an in-depth understanding of the physics and behaviour of such materials. While theoretical tools exist, they are often limited to simple cases. Thus, computational methods are necessary to model the complex unsteady physics of hydrogels with high fidelity. Mesoscale modelling is an emerging approach that enables simulations of polymeric structures at length and time scales in between those of molecular dynamics and continuum methods. In this feature article, we review various computational approaches to model responsive hydrogels and specifically focus on dissipative particle dynamics (DPD), a particle-based mesoscale method. We discuss several approaches for modelling cross-linked polymer networks in DPD, and describe recent applications of DPD to modelling hydrogel systems.