Algorithms to simulate the statistical microphysical and optical models for aerosol and polar stratospheric cloud (PSC) are described. Examples of such models for stratospheric and tropospheric aerosols and PSC are given. Different ways of applying the statistical aerosol and cloud models are discussed: - optimal parameterization of spectral dependences of aerosol extinction coefficient using the natural orthogonal basis; - multiple regression for estimating the optical parameter from measured one (for example, estimation of scattering coefficients from SAGE III multiwavelength measurements of aerosol extinction coefficients); - retrieval of microphysical properties of stratospheric aerosol and PSC from SAGE III extinction measurements; - lidar sounding.