The chemistry of hypervalent iodine(III) compounds has gained great interest over the past 30 years. Hypervalent iodine(III) compounds show valuable ionic reactivity due to their high electrophilicity but also express radical reactivity as single electron oxidants for carbon and heteroatom radical generation. Looking at ionic chemistry, these iodine(III) reagents can act as electrophiles to efficiently construct C-CF3, X-CF3 (X = heteroatom), C-Rf (Rf = perfluoroalkyl), X-Rf, C-N3, C-CN, S-CN, and C-X bonds. In some cases, a Lewis or a Bronsted acid is necessary to increase their electrophilicity. In these transformations, the iodine(III) compounds react as formal "CF3+", "Rf+", "N3+", "Ar+", "CN+", and "X+" equivalents. On the other hand, one electron reduction of the I(III) reagents opens the door to the radical world, which is the topic of this Account that focuses on radical reactivity of hypervalent iodine(III) compounds such as the Togni reagent, Zhdankin reagent, diaryliodonium salts, aryliodonium ylides, aryl(cyano)iodonium triflates, and aryl(perfluoroalkyl)iodonium triflates. Radical generation starting with I(III) reagents can also occur via thermal or light mediated homolysis of the weak hypervalent bond in such reagents. This reactivity can be used for alkane C-H functionalization. We will address important pioneering work in the area but will mainly focus on studies that have been conducted by our group over the last 5 years. We entered the field by investigating transition metal free single electron reduction of Togni type reagents using the readily available sodium 2,2,6,6-tetramethylpiperidine-1-oxyl salt (TEMPONa) as an organic one electron reductant for clean generation of the trifluoromethyl radical and perfluoroalkyl radicals. That valuable approach was later successfully also applied to the generation of azidyl and aryl radicals starting with the corresponding benziodoxole (Zhdankin reagent) and iodonium salts. In the presence of alkenes as radical acceptors, vicinal trifluoromethyl-, azido-, and arylaminoxylation products result via a sequence comprising radical addition to the alkene and subsequent TEMPO trapping. Electron-rich arenes also react with I(III) reagents via single electron transfer (SET) to give arene radical cations, which can then engage in arylation reactions. We also recognized that the isonitrile functionality in aryl isonitriles is a highly efficient perfluoroalkyl radical acceptor, and reaction of Rf-benziodoxoles (Togni type reagents) in the presence of a radical initiator provides various perfluoroalkylated N-heterocycles (indoles, phenanthridines, quinolines, etc.). We further found that aryliodonium ylides, previously used as carbene precursors in metal-mediated cyclopropanation reactions, react via SET reduction with TEMPONa to the corresponding aryl radicals. As a drawback of all these transformations, we realized that only one ligand of the iodine(III) reagent gets transferred to the substrate. To further increase atom-economy of such conversions, we identified cyano or perfluoroalkyl iodonium triflate salts as valuable reagents for stereoselective vicinal alkyne difunctionalization, where two ligands from the I(III) reagent are sequentially transferred to an alkyne acceptor. Finally, we will discuss alkynyl-benziodoxoles as radical acceptors for alkynylation reactions. Similar reactivity was found for the Zhdankin reagent that has been successfully applied to azidation of C-radicals, and also cyanation is possible with a cyano I(III) reagent. To summarize, this Account focuses on the design, development, mechanistic understanding, and synthetic application of hypervalent iodine(III) reagents in radical chemistry. [ABSTRACT FROM AUTHOR]