The paper is focused on inertia effects among drops moving within a turbulent cloud on size distribution evolution and formation of rain. Two related mechanisms are discussed: (1) the occurrence of inertia-induced relative velocities between drops falling within a turbulent flow, and (2) the tendency of inertial drops to concentrate within certain areas of turbulent flow with a corresponding concentration decrease elsewhere. It is shown that these turbulence-induced mechanisms lead to a broadening of the droplet spectrum during the early stages of cloud formation. Turbulence also decreases the minimum size of droplets are able to collide with the smaller ones. Thus, turbulence seems to bridge drop growth by condensation and coagulation. Due to the non-linear nature of the kinetic equation of coalescence, effects of positive fluctuations of drop concentration dominate and lead to a faster droplet spectrum broadening. Turbulence effects for ice particles, especially ice crystals and snowflakes, are expected to be much more pronounced than those demonstrated for water drops, because of a smaller terminal fall velocity of ice particles and a comparably large mass. Large turbulent eddies can concentrate ice crystals within certain areas, where ice crystals concentration will be substantially greater than mean ice crystal concentration. Thus, turbulence can contribute to the formation of high ice crystal concentration observed in mixed-phase clouds. The investigation of turbulence effects in clouds drop evolution is a held currently undergoing very rapid development. Some unsolved problems are discussed.