Humanitys interest in manufacturing silica-glass objects extends back over three thousand years. Silica glass is resistant to heating and exposure to many chemicals, and it is transparent in a wide wavelength range. Due to these qualities, silica glass is used for a variety of applications that shape our modern life, such as optical fibers in medicine and telecommunications. However, its chemical stability and brittleness impede the structuring of silica glass, especially on the small scale. Techniques for three-dimensional (3D) printing of silica glass, such as stereolithography and direct ink writing, have recently been demonstrated, but the achievable minimum feature size is several tens of micrometers. While submicrometric silica-glass structures have many interesting applications, for example in micro-optics, they are currently manufactured using lithography techniques, which severely limits the 3D shapes that can be realized. Here, we show 3D printing of optically transparent silica-glass structures with submicrometric features. We achieve this by cross-linking hydrogen silsesquioxane to silica glass using nonlinear absorption of laser light followed by the dissolution of the unexposed material. We print a functional microtoroid resonator with out-of-plane fiber couplers to demonstrate the new possibilities for designing and building silica-glass microdevices in 3D.