Polymersomes are bilayer vesicles, self-assembled from amphiphilic block copolymers. They are versatile nanocapsules with adjustable properties, such as flexibility, permeability, size and functionality. However, so far no methodological approach to control their shape exists. Here we demonstrate a mechanistically fully understood procedure to precisely control polymersome shape via an out-of-equilibrium process. Carefully selecting osmotic pressure and permeability initiates controlled deflation, resulting in transient capsule shapes, followed by reinflation of the polymersomes. The shape transformation towards stomatocytes, bowl-shaped vesicles, was probed with magnetic birefringence, permitting us to stop the process at any intermediate shape in the phase diagram. Quantitative electron microscopy analysis of the different morphologies reveals that this shape transformation proceeds via a long-predicted hysteretic deflation-inflation trajectory, which can be understood in terms of bending energy. Because of the high degree of controllability and predictability, this study provides the design rules for accessing polymersomes with all possible different shapes.