Glass is increasingly desired as a material for manufacturing complex microscopic geometries, from the micro-optics in compact consumer products to microfluidic systems for chemical synthesis and biological analyses. As the size, geometric, surface roughness, and mechanical strength requirements of glass evolve, conventional processing methods are challenged. We introduce microscale computed axial lithography (micro-CAL) of fused silica components, by tomographically illuminating a photopolymer-silica nanocomposite that is then sintered. We fabricated three-dimensional microfluidics with internal diameters of 150 micrometers, free-form micro-optical elements with a surface roughness of 6 nanometers, and complex high-strength trusses and lattice structures with minimum feature sizes of 50 micrometers. As a high-speed, layer-free digital light manufacturing process, micro-CAL can process nanocomposites with high solids content and high geometric freedom, enabling new device structures and applications.