The digital fabrication of oxide glasses by three-dimensional (3D) printing represents a major paradigm shift in the way glasses are designed and manufactured, opening opportunities to explore functionalities inaccessible by current technologies. The few enticing examples of 3D printed glasses are limited in their chemical compositions and suffer from the low resolution achievable with particle-based or molten glass technologies. Here, we report a digital light-processing 3D printing platform that exploits the photopolymerization-induced phase separation of hybrid resins to create glass parts with complex shapes, high spatial resolutions and multi-oxide chemical compositions. Analogously to conventional porous glass fabrication methods, we exploit phase separation phenomena to fabricate complex glass parts displaying light-controlled multiscale porosity and dense multicomponent transparent glasses with arbitrary geometry using a desktop printer. Because most functional properties of glasses emerge from their transparency and multicomponent nature, this 3D printing platform may be useful for distinct technologies, sciences and arts.