C–H functionalization reactions are playing an increasing role in the preparation and modification of complex organic molecules, including pharmaceuticals, agrochemicals and polymer precursors. In recent years, there have been many reports of radical C–H functionalization reactions initiated by hydrogen-atom transfer and proceeding via open-shell radical intermediates. These methods introduce strategic opportunities to functionalize C(sp3)–H bonds. Examples include synthetically useful advances in radical-chain reactivity and biomimetic radical-rebound reactions. A growing number of reactions, however, have been found to proceed via radical relay, whereby hydrogen-atom transfer generates a diffusible radical that is functionalized by a separate reagent or catalyst. The latter methods provide the basis for versatile C–H cross-coupling methods with diverse partners. In this Review, we highlight recent examples of radical-chain and radical-rebound methods to provide context for a survey of emerging radical-relay methods, which greatly expand the scope and utility of intermolecular C(sp3)–H functionalization and cross coupling. [Figure not available: see fulltext.]