In many situations in biology it is useful to consider a model that represents space as a grid of sites, each of which can be in one of a finite number of states and changes at a rate that depends on the state of finitely many neighbors. Durrett and Levin proposed in 1994 that the behavior of these systems can be inferred by looking at the associated "mean field" ODE that is obtained by pretending that all sites are always independent. We will describe the answers that result from this approach for a number of systems of interest in biology and illustrate our results by a videotape of computer simulations.