The use of bandwidth for mobile and cellular networks has been increasing at an unprecedented rate, with applications in emergent areas such as smart vehicles and civil infrastructure, telemedicine, and remote education. The predicted increase of mobile network utilisation requires a high data rate capacity to transfer information through the network. The current limited capacity of the fourth generation (4G) mobile network is not expected to satisfy the predicted high data demand by 2020. To meet this requirement, a new fifth generation (5G) mobile network has been proposed. In order to reach the high capacity demands, the 5G requires a wide frequency bandwidth, which is not available in the sub-3 GHz frequency spectrum. Therefore, many international organisations have assigned the millimetre-wave band (mm-Wave), which includes 24, 28, 37, 39, and 60 GHz, as a frequency band for 5G. Using mm-Wave raises many challenges such as an increase in the path loss, radiation field absorbed by the human body, signal polarisation misalignment, and MIMO antenna footprint inside the mobile handset. Therefore, designing beam-steering, reconfigurable circular polarization, and compact MIMO antenna systems for 5G applications is important to cope with these challenges. Although there are some antenna systems were reported recently for mm-Wave 5G, they had limited steering angles, one polarization types or bulky antenna size. This thesis aims to solve the current challenges mentioned above by developing mm-Wave 5G antenna systems and in doing so makes three main contributions to the field of mm-Wave 5G antenna systems.