A display may have an array of pixels with light-emitting diodes that emit light to form images. The display may have a substrate with thin-film transistor circuitry for supplying signals to the light-emitting diodes. Anodes may be formed on the thin-film transistor circuitry, emissive material may be formed on the anodes, and a cathode layer may overlap the anodes. During operation, currents may flow between the anodes and the cathode layer to illuminate the diodes. An array of electrical components such as an array of light sensors in an integrated circuit may be mounted under the substrate. An array of corresponding light transmitting windows may be formed in the display each of which may allow light to pass through the display to a corresponding one of the light sensors. Light transmitting windows may be formed by patterning the cathode layer and supplying the windows with antireflection layers.