The present paper considers the works on the development of SL-AV atmosphere model during last decade and their results. Different versions of the model applied for operational medium- and long-range forecasting are presented. The results are illustrated with the error evolution plots for the forecasts of different meteorological fields over the period of 2012-2019. The plans for a further model development are presented: in particular, works on the development of the new generation global atmosphere model based on the full nonhydrostatic equations. The approaches selected for the development of the future model dynamical core are described.