We introduce recent work studying systems of diffusion that interact through their reflection term (local time). We discuss how the hydrodynamic limit of such systems, i.e. the large-scale behavior of the empirical process, will converge to a nonlinear PDE whose solution exhibits interaction with the past values at the boundary. We will give several examples of interacting particle systems and their PDE limits, some of which include a free boundary component. If time allows, we will discuss aspects of the proofs and how the uniqueness of such PDEs follows from a stochastic representation.