An electronic device may have a glass housing structures. The glass housing structures may be used to cover a display and other internal electronic device components. The glass housing structure may have multiple glass pieces that are joined using a glass fusing process. A peripheral glass member may be fused along the edge of a planar glass member to enhance the thickness of the edge. A rounded edge feature may be formed by machining the thickened edge. Raised fused glass features may surround openings in the planar glass member. Multiple planar glass members may be fused together to form a five-sided box in which electronic components may be mounted. Raised support structure ribs may be formed by fusing glass structures to a planar glass member. Opaque masking material and colored glass may be used to create portions of the glass housing structures that hide internal device components from view.