Glass is one of the most important high-performance materials used for scientific research, in industry and in society, mainly owing to its unmatched optical transparency, outstanding mechanical, chemical and thermal resistance as well as its thermal and electrical insulating properties. However, glasses and especially high-purity glasses such as fused silica glass are notoriously difficult to shape, requiring high-temperature melting and casting processes for macroscopic objects or hazardous chemicals for microscopic features. These drawbacks have made glasses inaccessible to modern manufacturing technologies such as three-dimensional printing (3D printing). Using a casting nanocomposite, here we create transparent fused silica glass components using stereolithography 3D printers at resolutions of a few tens of micrometres. The process uses a photocurable silica nanocomposite that is 3D printed and converted to high-quality fused silica glass via heat treatment. The printed fused silica glass is non-porous, with the optical transparency of commercial fused silica glass, and has a smooth surface with a roughness of a few nanometres. By doping with metal salts, coloured glasses can be created. This work widens the choice of materials for 3D printing, enabling the creation of arbitrary macro- and microstructures in fused silica glass for many applications in both industry and academia.