An electronic device may be provided with a display having substrate layers such as a glass color filter layer substrate and a glass thin-film-transistor layer substrate. Display layers such as first and second layers of polymer, a liquid crystal layer interposed between the layers of polymer, color filter elements, and thin-film-transistor circuitry may be formed between the color filter layer substrate and the thin-film-transistor layer substrate. Flexible inactive portions of the display layers may protrude outward from between the color filter layer substrate and the thin-film-transistor substrate. Touch sensor circuitry may be formed from a flexible polymer substrate. The touch sensor circuitry may include conductive touch sensor lines and capacitive electrodes. Each conductive line may be coupled to only a single end of a respective one of the capacitive electrodes.