The assumptions, techniques and methods of improving Gaussian plume modeling are briefly reviewed. Then the statistical theory for the diffusion of a substance S into a turbulent flow in homogeneous and inhomogeneous flows, and neutral and stably stratified flows is introduced. In stably stratified flows the mixing of the temperature and the substance S between fluid elements is of critical importance in determining the growth of a plume, so that the plume's depth is not in general determined by the displacements of fluid elements through the source, not by the conventional Lagrangian statistics. But the plume depth, far downwind of the source, can be related to the local thermal diffusivity in the atmospheric boundary layer. The conditions are deduced under which this result can be used in stable conditions. The structure of turbulence in the stable boundary layer (SBL) is discussed.