Since there is the excellent summary on stellar convection given by J.-C. Pecker at the Liège symposium on stellar evolution in 1959, where he gives a complete account of the existing literature, I shall in this summary not try to do justice to the history of stellar convection research nor shall I try to mention all the existing papers even if they are quite important. I shall rather attempt to give an objective picture of the present state of affairs in order to be able to discuss our problems with the aerodynamicists. I shall cite only those papers that have been explicitly used for the results presented here. Additional references to literature may be found in the article by J.-C. Pecker.