Clouds contain fine water droplets in moist air, that may grow to form rain drops. A precise and quantitative understanding of the growth of droplets remains elusive, despite the fact that the essential physical mechanisms responsible for the process are known. In particular, the accepted scenario of rain formation has long rested on the notion of droplets of different sizes falling at different terminal velocities in a quiescent fluid, therefore colliding and coalescing. It has been realized that such approaches lead to wrong predictions of the time it takes for rain to form, in particular in warm clouds. The turbulent motion of air in clouds is likely to play an important role in the formation of rain drops. I will review in this talk the physical effects induced by turbulence, acting on particles that are much heavier than the surrounding fluids, such as water droplets in air. The main ones are preferential concentration -- the very uneven distribution of droplets, as well as the formation of "caustics". These effects lead to a strong enhancement of collision rates, which can play an important role in enhancing the rate of drop formation in clouds. I will also discuss some of the current experimental efforts to document the role of turbulence in cloud microphysics.