Iodosylbenzene reacts with various (pseudo)halides (trimethylsilyl azide or isocyanate or potassium azide, cyanate, and bromide) to yield unstable hypervalent iodine(III) compounds, PhIX2 (X = (pseudo)halide), that undergo rapid homolysis of the hypervalent I-X bonds and generate (pseudo)halide radicals, which can initiate the polymerization of styrene, (meth)acrylates, and vinyl esters. Polymers are formed containing (pseudo)halide functionalities at the α-chain end but, depending on the termination mechanism and the occurrence of transfer of (pseudo)halide groups from the initiator to the propagating radicals, also at the ω-chain end. With slowly polymerizing monomers (styrene and methyl methacrylate) and initiators that were generated rapidly at high concentrations and were especially unstable, the reactions proceeded via a "dead-end" polymerization mechanism, and only low to moderate monomer conversions were attained. When the initiator was generated more slowly and continuously throughout the polymerization (using the combination of iodosylbenzene with the poorly soluble potassium (pseudo)halide salts), typically higher conversions and higher molecular weights were reached. The presence of (pseudo)halide functionalities in the polymers was proved by elemental analysis, IR, and NMR spectroscopy. The azide-containing polymers underwent click-type coupling reactions with dialkynes, while the (iso)cyanate-containing polymers reacted with diamines to afford high-molecular-weight polymers with triazole- and urea-type interchain links, respectively.