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Millimetre-wave (mmWave) wireless communications has attracted great interest in recent years as a promising technology that can provide high data rate beyond 5G. Circular Polarization (CP) radiation is preferable to Linear Polarization (LP) in mmWave wireless communications, owing to the reliability of the wireless link it provides to suppress multi-path fading and polarization misalignment. Apart from the link robustness, high link capacity is also desirable by introducing technologies such as Polarization Division Multiplexing (PDM) or In-Band Full-Duplex (IBFD). Therefore, this research aims to design dual-circular-polarization (dual-CP) antennas with wide bandwidth and high port isolation to enable PDM or IBFD for mmWave wireless communications thereby achieving twofold spectral e ciency. The research work has been conducted in the following four parts. Firstly, a dual-CP horn antenna based on a stepped septum polarizer is designed in the W-band. By optimising the horn pro le, a wide bandwidth with good isolation is achieved in simulation and veri ed in experiment. Secondly, to further push the limits of the dual-CP antenna based on the stepped septum polarizer, a grooved-wall septum polarizer is proposed for the rst time with a 2-step design method to realize a dual-CP antenna with wider operating bandwidth and higher port isolation. Thirdly, in order to ease the fabrication di culty and further improve the antenna performance, a novel grooved-wall CP horn antenna is designed in simulation and veri ed in experiment in the W-band. The dual CP performance can be generated when used with an Orthomode Transducer (OMT), instead of a septum. Finally, this septum-free approach has been generalised to design a multi-section groovedi wall CP horn antenna with a low re ection coe cient over a wide bandwidth in the W-band. This horn antenna is demonstrated to be capable of achieving dual-CP with high isolation over a wide bandwidth when used together with an OMT.