AbstractA review of basic numerical simulation results on the processes in heavy ion thermonuclear fusion targets obtained with two-dimensional and three-dimensional codes for gas dynamic flows and radiation transport is given. A cylindrical target was studied that is compatible with the heavy ion accelerator scheme suggested by ITEP (Moscow). We also report on studies of an ellipsoidal target suggested by the group at Frankfurt University. Also, certain results of experiments at the Iskra-5 facilty are presented. Some aspects of these studies are described in more detail in separate articles in this volume (A.A. Basin et al., Fus. Eng. Des. 32–33 (1996) 603; V.V. Vatulin et al., Fus. Eng. Des. 32–33 (1996) 609).