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We introduce the concept of quantum printing -- the imprinting of quantum states from photons and phonons onto quantum matter. The discussion is focusing on charged fluids (metals, superconductors, Hall fluids) and neutral systems (magnets, excitons). We demonstrate how structured light can generate topological excitations, including vortices in superconductors and skyrmions in magnets. We also discuss how quantum printing induces magnetization in quantum paraelectrics and strain-mediated magnetization in Dirac materials. Finally, we propose future applications, such as printing entangled photon states, creating entangled topological excitations, and discuss applications of quantum printing to light induced quantum turbulence in a charged fluid. This review represents the expanded version of the shorter review submitted to Nature Physics.