This two-part paper outlines the present approach to the method of capillary electrophoresis and its place among other methods of analytical chemistry, in particular, as compared to liquid chromatography. The most efficient instrumental embodiments of capillary electrophoresis are considered: from the Nanofor series instruments to microchips. The first part is devoted to classical realizations of high-performance capillary electrophoresis (HPCE), their applications, evolution of the method toward multicapillary electrophoresis stimulated by the problem of DNA decoding. An overview of sequencing techniques is given.