The modeling of pedestrian motion is of great theoretical and practical interest. Recent experimental efforts have revealed quantitative details of pedestrian interactions, which have been successfully cast into mathematical equations. Furthermore, corresponding computer simulations of large numbers of pedestrians have been compared with the empirically observed dynamics of crowds. Such studies have led to a deeper understanding of how collective behavior on a macroscopic scale emerges from individual human interactions. Interestingly enough, the non-linear interactions of pedestrians lead to various complex, spatio-temporal pattern-formation phenomena. This includes the emergence of lanes of uniform walking direction, oscillations of the pedestrian flow at bottlenecks, and the formation of stripes in two intersecting flows. Such self-organized patterns of motion demonstrate that an efficient, “intelligent” collective dynamics can be based on simple, local interactions. Under extreme conditions, however, coordination may break down, giving rise to critical crowd conditions. Examples are “freezing-by-heating” and “faster-is-slower” effects, but also the transition to “turbulent” crowd dynamics. These observations have important implications for the optimization of pedestrian facilities, in particular for evacuation situations.