After decades focusing on the molecular and genetic aspects of organogenesis, researchers are showing renewed interest in the physical mechanisms that create organs. This review deals with the mechanical processes involved in constructing the heart and brain, concentrating primarily on cardiac looping, shaping of the primitive brain tube, and folding of the cerebral cortex. Recent studies suggest that differential growth drives large-scale shape changes in all three problems, causing the heart and brain tubes to bend and the cerebral cortex to buckle. Relatively local changes in form involve other mechanisms such as differential contraction. Understanding the mechanics of organogenesis is central to determining the link between genetics and the biophysical creation of form and structure.