Dendrimers, the aesthetically beautiful macromolecules displaying a variety of potentially useful architecture-induced properties, are traditionally assembled in solution. However, since 1988, a number of dendritic structures have been assembled on insoluble organic and inorganic polymers, and thus dendronized supports have been formed. One of the major applications of these new materials is in the field of heterogeneous catalysis. Supported dendritic catalytic systems, bearing the catalytic units on the dendron periphery, have been examined in the last 5 years in such reactions as hydroformylation, Heck and other Pd-catalyzed C-C bond formations, oxidation, and en anti oselective addition to aldehydes. In the majority of these studies, substantial dendritic effects on the reactivity, selectivity, or recyclability of the catalysts were observed. Although a number of factors have been suggested as sources of the effects, it is most likely that the phenomenon has a multicomponent origin. Additional research, including a full determination of the effects and their causes, is likely to lead to markedly better heterogeneous catalytic Systems. (C) 2004 Wiley Periodicals, Inc.