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Fabrication goes for a quick spin Most 3D printing techniques involve adding material layer by layer. This sets some limitations on the types of applications for which 3D printing is suitable, such as printing around a preexisting object. Kelly et al. present a different method for manufacturing by rotating a photopolymer in a dynamically evolving light field (see the Perspective by Hart and Rao). This allowed them to print entire complex objects through one complete revolution, circumventing the need for layering. The method may be particularly useful for high-viscosity photopolymers and multimaterial fabrication. Science, this issue p. 1075; see also p. 1042 Exposing a rotating photopolymer to a dynamically evolving light pattern achieves 3D printing without layer-by-layer assembly. Additive manufacturing promises enormous geometrical freedom and the potential to combine materials for complex functions. The speed, geometry, and surface quality limitations of additive processes are linked to their reliance on material layering. We demonstrated concurrent printing of all points within a three-dimensional object by illuminating a rotating volume of photosensitive material with a dynamically evolving light pattern. We printed features as small as 0.3 millimeters in engineering acrylate polymers and printed soft structures with exceptionally smooth surfaces into a gelatin methacrylate hydrogel. Our process enables us to construct components that encase other preexisting solid objects, allowing for multimaterial fabrication. We developed models to describe speed and spatial resolution capabilities and demonstrated printing times of 30 to 120 seconds for diverse centimeter-scale objects.