Electronic devices are provided that contain wireless communications circuitry. The wireless communications circuitry may have antenna diversity circuitry that allows an optimum antenna in an antenna structure to be switched into use during device operations. The antenna structure may be shared between multiple radio-frequency transceivers in a radio-frequency transceiver circuit. The radio-frequency transceiver circuit may be coupled to the antenna structure using switching and filtering circuitry. The filtering circuitry may include a diplexer that divides radio-frequency signals into a divided signal path based on frequency. The filtering circuitry may also include bandpass filters that are interposed in each branch of the divided signal path. Switching circuitry in the switching and filtering circuitry may be used to selectively configure the wireless communications circuitry in transmit and receive modes using multiple communications bands.