Electronic devices are provided that contain wireless communications circuitry. The wireless communications circuitry may have antenna diversity circuitry that allows an optimum antenna or optimum antennas 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 one or more diplexers that divide radio-frequency signals into divided signal paths based on frequency. The filtering circuitry may also include low pass, high pass, and bandpass filters that are interposed in the divided signal paths. 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.