This dissertation aims to explore the design trade-offs and technological limitations of planar antenna elements and arrays for Ka-band space applications. The motivation for this research stems from the growing importance of wideband millimetre wave radio communication systems able to provide very high transmission rates. Part of the work has been carried out in the framework of a European Space Agency research project, which has provided very realistic and demanding specifications. Two different antenna array concepts are proposed. The first one has been developed to provide optimised RF performance and miniaturised size. The second one has been designed to be fabricated using only cheap and simple manufacturing techniques. In this way, the trade-offs between performance, size and fabrication complexity are studied. Prototypes of both solutions have been fabricated and tested. They exhibit wide impedance bandwidth and shaped radiation patterns with circular polarisation. The radiation efficiency is over 70% for the first array and over 60% in the second solution, which are good figures at Ka-band frequencies. Additionally and connected with the development of the antenna array solutions, several novel Ka-band RF components and circularly polarised radiating elements are proposed. Finally, a methodology to synthesise antenna arrays with complex requirements is also presented