Interacting particle systems is by now a mature area of probability
theory, but one that is still very active. We begin this paper by explaining
how models from this area arise in fields such as physics and biology. We turn
then to a discussion of both older and more recent results about them,
concentrating on contact processes, voter models, and exclusion processes.
These processes are among the most studied in the field, and have the virtue of
relative simplicity in their description, which permits us to address the
fundamental issues about their behavior without dealing with the extra
complications that models from specific areas of application would require.