Over the past 100 years particle collision models for a range of particle inertias and carrier fluid flow conditions have been developed. Models for perikinetic and orthokinetic collisions for simple, laminar shear flows as well as collisions associated with differential sedimentation are well documented. Collision models developed for turbulent flow conditions are demarcated on the one side with the model of Saffman and Turner (1956) associated with particles exhibiting zero inertia and on the other side with the model of Abrahamson (1975) for particle velocities that are completely decorrelated from the carrier fluid velocities. Various attempts have been made to develop universal collision models that span the entire range of inertias in a turbulent flow field. It is a well-accepted fact that models based on a cylindrical as opposed to a spherical formulation are erroneous. Furthermore, the collision frequency of particles exhibiting identical inertias are not negligible. Particles exhibiting relaxation times close to the Kolmogorov time scale of the turbulent flow are subject to preferential concentration that could increase the collision frequency by up to two orders of magnitude. In recent years the direct numerical simulation (DNS) of colliding particles in a turbulent flow field have been preferred as a means to secure the collision data on which the collision models are based. The primary advantage of the numerical treatment is better control over flow and particle variables as well as more accurate collision statistics. However, a numerical treatment places a severe restriction on the magnitude of the turbulent flow Reynolds number. The future development of more comprehensive and accurate collision models will most likely keep pace with the growth in computational resources. (C) 2011 Elsevier Ltd. All rights reserved.