This paper is concerned with meteorological processes that may have an influence on the occurrence of episodes of high pollution involving chimney plumes. It reviews meteorological mechanisms that could lead to or maintain high concentrations at distances beyond the range normally considered in dispersion models (distances greater than 30 km). Fundamental parameters of the atmospheric boundary layer are shown to largely determine short-range and long-range dispersion, but their values are usually not well known in specific cases. A simple estimate is provided of the magnitude of the maximum hourly average concentrations during a long-range fumigation episode from a tall stack.