Large-scale systems of interacting particles are ubiquitous in several relevant applications (in fact, the term particle may stand for actual particles, individuals, animals, parameters in neural networks, etc?). In many circumstances, it may be convenient to describe such particle systems on the continuum scale, i.e., to view their empirical density as the solution of suitable stochastic PDEs. This way of looking at particle systems has given rise to the theory nowadays referred to as Fluctuating Hydrodynamics (FH). In this talk, I plan to (1) give a brief overview of the theory of FH, and (2) discuss high-order numerical discretisations and variance reduction techniques for the Dean-Kawasaki model, a prototype model of FH (based on joint works with Julian Fischer, Jonas Ingmanns, Claudia Raithel)