An electronic device may have a display mounted in a housing. The display may have layers such as polarizer layers, a color filter layer, and a thin-film transistor layer. Display layers such as color filter layers and thin-film-transistor layers may have glass substrates. Notches or other openings may be formed in the layers of a display. For example, a notch with a curved chamfered edge may be formed in a lower end of a thin-film-transistor layer. A component such as a button may overlap the notch. Structures such as sensors, cameras, acoustic components, and other electronic components, buttons, communications path structures such as flexible printed circuit cables and wire bonding wires, and housing structures may be received within a display layer notch.