Road traffic may be studied by a wide spectrum of methods, ranging from models that aim at a maximum of realism to others that try to capture only the most characteristic traits. The latter category has since many years attracted the attention of statistical physicists, for whom the challenge resides in the analogy with interacting many-particle system and nonequilibrium phase transitions. This talk will present one such model. It describes the crossing of two unidirectional flows of pedestrians represented by hard core particles moving on a lattice. The two basic model parameters are the width $M$ of the crossing streets and the pedestrian flow density $alpha$. par We will discuss in particular (i) the jamming transition that occurs at high flow rate; and (ii) pattern formation appearing at lower flow rate. This work is based on an ongoing collaboration with Julien Cividini and Cécile Appert-Rolland.