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The paper provides a review of current research on microwave reflector antennas with particular regard to those antennas which produce pencil-beam radiation patterns. After a preliminary examination of microwave antennas of different types attention is focused on circularly symmetric antennas with axially symmetric feed systems. This class of antenna accounts for the largest number of applications which include microwave point-to-point communication, satellite communication, and radio astronomy. The choice of optimum feed is considered in more detail and it is demonstrated that metallic feeds with corrugated walls represent the best choice in most cases. Brief reference is also made to dielectric cone feeds which may find a place in future systems. The design of dual-reflector systems is considered in depth and different computer optimisation techniques are reviewed. These include the latest methods of diffraction optimization in which more than one of the antenna specifications is involved. An example is given where efficiency and VSWR are simultaneously optimized.