Organocobalt(III) complexes (R-Co-III), defined as cobalt complexes featuring a carbon cobalt bond, are largely used to produce carbon-centered radicals by homolytic cleavage of their C-Co bond under mild conditions. They are key compounds in cutting-edge developments in the fields of organic chemistry, biochemistry, medical research, radical reactions, and organometallic chemistry. This is the first Review of the use of R-Co-III in both organic and polymer chemistries. Although pioneering works in organic synthesis have largely contributed to the implementation of R-Co-III in polymer design, the two fields have evolved independently, with many breakthroughs on both sides. The main motivation of this Review is to confront both fields to stimulate cross-fertilization. It notably describes the most important synthetic pathways for R-Co-III, the influence of the ligand structure and the environment of the complex on the C-Co bond strength, the modes of formation of the radicals, and the most relevant R-Co-III-promoted radical reactions, with a focus on the main reaction mechanisms.