The Butler matrix is a passive beamforming network that has become the most widely adopted architecture for phased antenna arrays due to its structural simplicity, theoretically lossless transmission, spatially orthogonal beams, and realizable bandwidth. Originally introduced by Butler and Lowe in 1961 as an extension of Blass’s matrix, the Butler matrix employs an N×N configuration of hybrid couplers and fixed phase shifters to generate progressive phase shifts across array elements, enabling precise beam steering through selective excitation of input ports. Beyond linear arrays, Sheleg demonstrated its rotational mechanism in cylindrical arrays, showing that the Butler matrix performs a spatial fast Fourier transform (FFT) to produce N orthogonal beams and cyclically permute outputs via input phase variation. This property allows rotation of radiation patterns around the azimuth without altering amplitude distributions, offering significant advantages for high-speed scanning in military and communication systems. This paper revisits the rotational mechanism of the Butler matrix, elucidating its theoretical foundation and practical implications, and provides a simplified framework for understanding its role in advanced beamforming applications.