The growing complexity of communication and surveillance systems means that there is an increasing need for antennas with multiple beam capability. Several technologies such as radio frequency (RF), intermediate frequency (IF), digital and optical are available to meet this need but RF beamforming has the advantage of simplicity and a good capability for many applications. This state of the art review of RF beamforming methods for multiple beam antennas aims to introduce the topic and to collate and classify types, giving a critical assessment of comparative performance. The fundamental relationship between the number of active control elements and the number of beams is taken as a measure of beamformer performance and this also indicates that, for a limited number of active elements, high gain antennas with narrow beams will have limited scan range whilst low gain systems have a wide angle capability. This deduction is reinforced by the practical results collected at the end of the review. The beamformer types covered include lens based beamformers such as the Ruze, Rotman, R-KR and nonuniform refractive index types together with objective lenses with separate feed arrays. Reflector based multiple beam antennas based on zero, one or two Fourier transform properties are followed by circuit types including the Blass and Butler matrices. The wide range of information presented is clarified by a summary section giving an indication of comparative performance levels. The very diversity of RF beamformer types and performance are seen to attest the importance of the topic area for current and future antenna systems and point the way to further innovation and development in this very significant field.