We will examine various situations in which large numbers of discrete objects are interacting. In many cases a continuum model can be formulated, in which the discrete objects are replaced by a density (or probability distribution function). We examine the relationship between the discrete and continuous models, focussing in particular on regions where the continuous model breaks down, and needs to be matched with a discrete local approximation. Examples are drawn from the theory of dislocations, superconductivity, and molecular reaction-diffusion.