A display may have an array of pixels controlled by display driver circuitry. The pixels may have pixel circuits. In liquid crystal display configurations, each pixel circuit may have an electrode that applies electric fields to an associated portion of a liquid crystal layer. In organic light-emitting diode displays, each pixel circuit may have a drive transistor that applies current to an organic light-emitting diode in the pixel circuit. The pixel circuits and display driver circuitry may have thin-film transistor circuitry that includes transistor such as silicon transistors and semiconducting-oxide transistors. Semiconducting-oxide transistors and silicon transistors may be formed on a common substrate. Semiconducting-oxide transistors may have polysilicon layers with doped regions that serve as gates. Semiconducting-oxide channel regions overlap the gates. Transparent conductive oxide and metal may be used to form source-drain terminals that are coupled to opposing edges of the semiconducting oxide channel regions.