An electronic device may be provided with a display. Standard and high dynamic range content may be produced by content generators operating on control circuitry. In a first mode of operation, standard dynamic range content is displayed. In a second mode of operation, high dynamic range content is displayed. In a third mode of operation, standard dynamic range content and high dynamic range content are simultaneously displayed. Tone mapping parameters may be produced by a tone mapping engine for use in displaying the standard and high dynamic range content. The tone mapping parameters may be selected based on factors such as ambient light level, user brightness setting, content statistics, and display characteristics. Tone mapping parameters may be selected to accommodate simultaneous display of standard and high dynamic range content and to accommodate transitions between standard and high dynamic range content.