It is well known that convective clouds play an essential role in the evolution of the aerosol particles in the atmosphere by providing spatial redistribution and transformation of aerosol due to in cloud chemical reactions, dynamical and microphysical processes. The influence of the clouds upon the aerosol properties increase greatly in extreme conditions, such as volcano eruptions, explosions, large fires, when enormous number of aerosol particles of different size and chemical compound are injected in the atmosphere. In this paper the overview of the main results, obtained by the authors in the field of numerical modeling of the convective clouds, developing in natural and extreme conditions and the investigation of their role in the evolution of the atmospheric aerosol is presented.