Although recent years have witnessed an impressive confluence of experiments and kinetic and statistical theories, presently there is no comprehensive understanding of the interrelation between chemical sequences in synthetic copolymers and the conditions of synthesis. For this problem, numerical simulations in conjunction with simple models provide a rather detailed answer. A survey is given of the simulation methods as applied to the design of nontrivial chemical sequences in copolymers obtained via heterogeneous radical polymerization. This review is focused on a recently developed approach, called conformation-dependent sequence design, which takes into account a strong coupling between the conformation and primary structure of copolymers during their synthesis. We consider some applications of this technique, including the following problems and systems: (1) the design of sequences with long-range correlations via solution radical copolymerization with simultaneous globule formation, (2) radical copolymerization near a chemically homogeneous surface leading to a copolymer with a gradient primary structure, and (3) template copolymerization near chemically patterned surfaces. (C) 2004 Wiley Periodicals, Inc.