In the last fifteen years, a large variety of specialty polymers of diverse chemical structure and functionality have been synthesized with the rhodium-based catalysts. The high tolerance to the reaction medium and functional groups of monomers, as well as ability to control various structure features of the polymer formed are typical properties of these catalysts. In addition, some rhodium catalysts can be anchored to inorganic or organic supports or dissolved in ionic liquids to form heterophase polymerization systems, which opens the way to pure, well-defined polymers free of the catalyst residues, as well as to recycling rhodium catalysts. This review provides a survey on the polymerization reactions induced with rhodium-based catalysts, in which one or more structure attributes of the polymer formed are subject to control. The structure attributes considered are (i) sequential arrangement of monomeric units along polymer chains; (ii) head-tail isomerism of polymer molecules; (iii) configurational structure of polymer molecules; (iv) conformation of polymer molecules; and (v) molecular weight and molecular-weight distribution of the polymer formed. A review with 188 references.