The goal of 3D printing is to realize complex 3D structures by locally adding material in small volume elements called voxels - in contrast to successively subtracting material by etching, milling or machining. This field started with optics-based proposals in the 1970s. Progress has required breakthroughs in physics, chemistry, materials science, laser science and engineering. This Review focuses on the physics underlying optics-based approaches, including interference lithography, tomographic volumetric additive manufacturing, stereolithography, continuous liquid-interface printing, light-sheet printing, parallelized spatiotemporal focusing and (multi-)focus scanning. Light-matter interactions that are discussed include one-photon, two-photon, multi-photon or cascaded nonlinear optical absorption processes for excitation and stimulated-emission depletion or excited-state absorption followed by reverse intersystem crossing for de-excitation. The future physics challenges lie in further boosting three metrics: spatial resolution, rate of voxel creation and range of available dissimilar material properties. Engineering challenges lie in achieving these metrics in compact, low-cost and low-energy-consumption instruments and in identifying new applications.|This Review categorizes the physics of many different light-based 3D printing modalities and expounds on the light-matter interactions required for the creation of (multi-)material 3D structures. An outlook is provided regarding key printing performance parameters and future directions.|Three-dimensional printing with light is an additive manufacturing process in which light irradiation locally adds a solid material (typically from a liquid 'ink'), rather than subtracting it from a solid by machining or drilling, to form complex 3D structures from the macroscale to the nanoscale.All current light-based 3D printing modalities (including interference lithography, spatial focusing, spatiotemporal focusing, tomographic volumetric additive manufacturing and layer-by-layer approaches) can be seen as approximations of an ideal light exposure scheme in which a tailored 3D pattern of light exposes an ink in a single shot.Light shone during 3D printing couples to the ink via electric-dipole-mediated light-matter interactions to dedicated trigger (photoinitiator) molecules; sometimes ordinary one-photon absorption suffices, yet often other processes such as multi-photon absorption or two-colour two-step absorption are needed to sufficiently localize the excitation in 3D space.Material formation from the ink following the light trigger is highly material dependent, with different chemical and physical processes involved for the formation of polymers, metals and semiconductors.Although researchers strive to improve the speed and resolution of 3D printing technologies, the formation of a certain voxel unavoidably requires delivering a certain light energy; therefore, increasing the number of voxels printed per unit time requires increasing light power.The challenges of 3D printing remain: enable ever finer feature sizes, increase print speed, open the door to more dissimilar materials and make 3D laser printers more compact and less expensive.