We review recent progress using numerical simulations as a testbed for development of a theory of stellar convection, much as envisaged by John von Newmann. Necessary features of the theory, non‐locality and fluctuations, are illustrated by computer movies. It is found that the common approximation of convection as a diffusive process presents the wrong physical picture, and improvements are suggested.New observational results discussed at the conference are gratifying in their validation of some of our theoretical ideas, especially the idea that SNIb and SNIc events are related to the explosion of massive star cores which have been stripped by mass loss and binary interactions [1]