An electronic device may have layers of glass for forming components such as a display. A display cover glass layer may overlap an array of pixels. A touch sensor may be formed under the display cover glass layer. Conductive structures such as transparent conductive electrodes or other conductive layers of material may be formed on the outer surface of the display cover glass layer. The electrodes on the outer surface of the display cover glass layer may be coupled to metal contacts and other circuitry on the inner surface of the display cover glass layer using conductive vias. Vias may be provided with barrier layers, opaque coatings, tapers, and other structures and may be formed using techniques that enhance compatibility with chemical strengthening processes.