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This thesis presents an efficient way to analyse and design linear-to-circular polarising reflector antennas comprising doubly periodic metallodielectric arrays. These type of structures, used in conjunction with subreflectors, has risen as a promising solution to reduce the number of reflectors in multi-beam antennas in single-feed-per beam architectures while providing circular polarisation for the downlink/uplink. The first part of the thesis is concerned with the analysis of single reflector antennas, focusing on their depolarisation properties. MATLAB® codes are developed to obtain the far-field from the reflector and are successfully compared against the preferred tool in the market for the analysis and design of reflector antennas, i.e.,TICRA's GRASP. This analysis tool is used in conjunction with a Floquet analysis of periodic structures to obtain the far-field from doubly periodic metallodielectric arrays. An efficient way to extract the fundamental modes from the near-field of the feed is introduced for cases where the the reflector is placed at the near-field of the feed. A design procedure to reduce the cross-polarisation of the polarising reflector far-field is included. This procedure is based on physical insight rather than brute-force optimisation, leading to computational efficiencies. Design examples are shown are compared against the original uniform unit-cell array design. Improvements up to 16 dB in the cross-polarisation levels across a wide bandwidth are achieved. The procedure is validated experimentally. The design procedure is also applied to a multi-beam case where three ideal sources are used to feed the reflector. Compared with the uniform unit-cell array, improvements up to 10 dB are obtained in the cross-polarisation performance for the whole bandwidth and the three feeds at the same time.