  Collisions between particles suspended in a fluid play an important role in
many physical processes. As an example, collisions of microscopic water
droplets in clouds are a necessary step in the production of macroscopic
raindrops. Collisions of dust grains are also conjectured to be important for
planet formation in the gas surrounding young stars, and also to play a role in
the dynamics of sand storms. In these processes, collisions are favoured by
fast turbulent motions. Here we review recent advances in the understanding of
collisional aggregation due to turbulence. We discuss the role of fractal
clustering of particles, and caustic singularities of their velocities. We also
discuss limitations of the Smoluchowski equation for modelling these processes.
These advances lead to a semi-quantitative understanding on the influence of
turbulence on collision rates, and point to deficiencies in the current
understanding of rainfall and planet formation.
