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This paper consists of three parts, each treating a single type of antenna scan. Part I is devoted to the spiral scan, deriving the equations of motion for searching a region of space in a minimum period of time. Power relations required for the antenna drive also are derived. Part II discusses a simple conical scan; the development concerns the optimum antenna gain, the gain at the edges of the region scanned, and the optimum wavelength. Part III pertains to sector scanning. The analysis of the variation of target illumination over the sector is presented for an antenna having simple harmonic motion. The critical angles for selection between a sector-scanning antenna and a uniformly rotating assembly of ``n'' antennas are derived. A figure of merit for sector scan having non-harmonic motion is defined.