Nanogels—internally crosslinked macromolecules—have a growing palette of potential applications, including as drug, gene or radioisotope nanocarriers and as in vivo signaling molecules in modern diagnostics and therapy. This has triggered considerable interest in developing new methods for their synthesis. The procedure based on intramolecular crosslinking of polymer radicals generated by pulses of ionizing radiation has many advantages. The substrates needed are usually simple biocompatible polymers and water. This eliminates the use of monomers, chemical crosslinking agents, initiators, surfactants, etc., thus limiting potential problems with the biocompatibility of products. This review summarizes the basics of this method, providing background information on relevant aspects of polymer solution thermodynamics, radiolysis of aqueous solutions, generation and reactions of polymer radicals, and the non-trivial kinetics and mechanism of crosslinking, focusing on the main factors influencing the outcomes of the radiation synthesis of nanogels: molecular weight of the starting polymer, its concentration, irradiation mode, absorbed dose of ionizing radiation and temperature. The most important techniques used to perform the synthesis, to study the kinetics and mechanism of the involved reactions, and to assess the physicochemical properties of the formed nanogels are presented. Two select important cases, the synthesis of nanogels based on polyvinylpyrrolidone (PVP) and/or poly(acrylic acid) (PAA), are discussed in more detail. Examples of recent application studies on radiation-synthesized PVP and PAA nanogels in transporting drugs across the blood–brain barrier and as targeted radioisotope carriers in nanoradiotherapy are briefly described.