Abstract: Discrete space-time models were introduced about 30 years ago by independently by the physicists Myrheim and t'Hooft. It later developed into the causal set theoretic approach to quantum gravity championed by R.Sorkin and his collaborators. As mathematical objects, discrete space times are partially ordered sets, with the partial order representing the relation of past-future in physics. We will describe the objects, present some basic results about them and show how they pop-up naturally in various applications. The talk will be self contained.