Consider n brownian motion particles on R, S1, or n discrete time random walks on a graph G. A ‘collision’occurs when two particles have the same position at the same time. Given a rule for modeling interactions between particles, we can analyze the long term behavior of such a system. We focus on the case where particles are independent, and briefly discuss variants, such as the situation where particles are conditioned not to collide; or when there is a repelling drift term between particles. We derive new formulas for collision times among two or three simple random walks on Z. Also, we review the existing literature to gain insight about other underlying graphs, and the case of multiple brownian particles.