<p>Photons can be structured in space and time, blending quantum information and structured light in the context of high-dimensional and multidimensional entanglement. This opens a pathway to richly textured Hilbert spaces, high-information-capacity photons and exciting applications that exploit the new multiple-degrees-of-freedom modalities of quantum structured light. Progress has accelerated of late, driven by a modern toolkit comprising both bulk and on-chip solutions, taming dimensionality and unlocking exciting applications from imaging and sensing to networks and communication. In this Review we aim to capture this exciting inflection point, where quantum structured light can finally be harnessed to realize its full potential.</p>