Key theoretical concepts advanced by the Bauman MSTU scientific school 'Zoom lens design' are discussed. These include methods for design of both classical and laser zoom lenses, systems with linear and nonlinear relations between the displacements of components, basics of professor I. I. Pakhomov's theory of generalized parameters, a method of paraxial synthesis of multicomponent zoom systems, a method of aberration synthesis of zoom systems in the approximation of the third- and fifth-order aberrations. The effectiveness of the described methods is illustrated by examples of designing zoom systems with superior optical characteristics.