An electronic device may have a display and other optical components such as optical sensors. The display and other components may be overlapped by chemically strengthened glass coherent fiber bundles. The surfaces of a coherent fiber bundle may include ion-exchanged glass that places theses surfaces under compressive stress. In some configurations, the coherent fiber bundle is symmetrically stressed and has equal amounts of compressive stress on opposing surfaces. In other configurations, the coherent fiber bundle is asymmetrically stressed and has more compressive stress on one surface than the other. The coherent fiber bundle may have areas with curved cross-sectional profiles, planar areas, and/or areas with compound curvature. Sensor windows may be formed in the coherent fiber bundle that are surrounded by an opaque area. When overlapping a display, the coherent fiber bundle may serve as a display cover glass layer.