The Canadian Centre for Climate Modelling and Analysis third generation atmospheric general circulation model (AGCM3) is described. The discussion summarizes the details of the complete physics package emphasizing the changes made relative to the second generation version of the model. AGCM3 is the underlying model for applications which include the IPCC fourth assessment, coupled atmosphere-ocean seasonal forecasting, the first generation of the CCCma earth system model (CanESM1), and middle-atmosphere chemical-climate modelling (CCM). Here we shall focus on issues related to an upwardly extended version of AGCM3, the Canadian Middle-Atmosphere Model (CMAM). The CCM version of CMAM participated in the 2006 WMO/UNEP Scientific Assessment of Ozone Depletion and issues concerning its climate such as the impact of gravity-wave drag, the modelling of a spontaneous QBO, and the seasonality of the breakdown of the Southern Hemisphere polar vortex are discussed here.