Understanding pedestrian dynamics is important for everyday life, e.g. to improve safety and comfort. In the last 25 years, important contributions have been made based on cellular automata models. The challenges faced in modeling pedestrian and crowd dynamics are discussed on the basis of empirical results and the observed collective phenomena. These provide benchmark tests for the modeling approaches. Meanwhile a zoo of models has been proposed. We briefly present the general model classes before focusing on cellular automata based models which by now have become a standard tool also for applications. The dynamics of the agents is usually based on simple stochastic rules that allow to include e.g. psychological aspects of the motion of individuals in a relatively simple way.