Vapour condensation in cloud cores produces small droplets that are close to one another in size. In warm clouds, droplets grow to raindrop size by coalescence due to collisions. Air turbulence is thought to be the main cause for collisions of close in size droplets exceeding radii of a few microns, and therefore rain prediction requires a quantitative description of droplet collision in turbulence. Turbulent vortices act as small centrifuges that spin heavy droplets out, creating concentration inhomogeneities and jets of droplets, both of which increase the mean collision rate. A formula for the collision rate of small heavy particles in a turbulent flow is to be decribed. Its derivation uses a formalism for tracing random trajectories recently developed in particularly by Russian-Israeli collaboration. I describe an enhancement of inertial effects by turbulence intermittency and an interplay between turbulence and gravity that determines the collision rate. I present a new mechanism, the `sling effect', for collisions due to jets of droplets detached from the air flow. Preliminary quantitative analysis shows that even moderate turbulence can substantially accelerate the transition from condensation to coalescence stage in the interval of few tens of microns. One concludes that air turbulence can substantially accelerate the appearance of large droplets that trigger rain.