The log-normal size distribution theories developed recently for aerosol coagulation are reviewed. The analytical solutiosn to Brownian coagulation developed recently for various particle size regimes are reviewed. In order to describe the evolution of the size distribution of a coagulating aerosol over the entire size range, the analytical solutions developed individually for the free-molecule regime, the transition regime, the nearcontinuum regime, and the continuum regime have been combined. The work described here represents the first analytical solution to the aerosol coagulation problem covering the entire particle size range.