After-action of the ideas of I.M. Lifshitz in polymer and biopolymer physics

We review the development of ideas in polymer physics initially formulated by I.M. Lifshitz. We start with general issues in polymer statistics, such as the analogy with quantum mechanics, and then continue with globules and a variety of coil-globule transitions, ranging from toroidal DNA particles, superabsorbing gels, to orientational order in liquid-crystalline polymers. We pay major attention to the more recent developments in the theory of heteropolymers with a quenched sequence of chemically distinct monomers and to the works on sequence design applied both in protein physics and in the attempts to mimic properties of proteins in synthetic copolymers.