In this article, recent examples are reviewed of late-transition-metal catalysis applied to polymer topology control. By the judicious selection or design of late-transition-metal catalysts, polymers with a broad range of topologies, including linear, short-chain-branched, hyperbranched, dendritic, and cyclic topologies, have been successfully synthesized. A distinctive advantage of the catalyst approach is that polymers with complex topologies can be prepared in one pot from simple commercial monomers. A fundamental difference of the catalyst approach with respect to other approaches is that the polymer topology is controlled by the catalysts instead of the monomer structure. In our own laboratory, we have successfully used two strategies to control the polymer topology with late-transition-metal catalysts. In the first strategy, hyperbranched polymers are prepared by the direct free-radical polymerization of divinyl monomers through control of the competition between propagation and chain transfer with a cobalt chain-transfer catalyst. In the second strategy, polyethylene topology is successfully controlled by the regulation of the competition between propagation and chain walking with the Brookhart Pd-II-alpha-bisimine catalyst. (C) 2003 Wiley Periodicals, Inc.