In the living cell, ionizing radiation can cause DNA damage by the direct effect (ionization of DNA) and the indirect effect (reaction of radicals formed in the neighborhood of DNA with DNA, e.g., OH, eaq-, H, protein- and glutathione-derived radicals). Properties of the base radical cations have been studied in model systems using SO4- radical to oxidize the nucleobases in aqueous solution. The pKa values of some nucleobase radical cations are reported, so are the ensuing reactions of the thymidine radical cation with water. The products of reactions are compared with those formed by OH radical attack. The reaction of eaq- with the nucleobases yields radical anions. Protonation at heteroatom sites and at carbon are discussed, and some recent results regarding the electron transfer to adjacent nucleobases as well as to 5-bromouracil are reported. A brief account is given on the reaction of carbon-centered radicals with the nucleobases. These reactions may mimic the reactions of protein-derived radicals with DNA. Glutathione is present in cells at rather high concentrations and is expected to act as an H- or electron-donor in repairing radiation-induced DNA damage (chemical repair). As thiyl radicals are known to also undergo the reverse reaction, i.e., H-abstraction from suitable solutes, some experiments are reported which probe this type of reaction with dilute DNA solutions. In some polynucleotides radical transfer from the base radical to the sugar moiety occurs with the consequence of strand breakage and base release. Some currently held mechanistic concepts are discussed. Attention is drawn to some important open questions which should be addressed in the near future.