Some of the background to radiation chemical studies of DNA damage is presented, followed by a review of measurements of such damage and its repair in mammalian cells. While most effort has been placed on the measurement of radiation-induced strand breaks (because assays can be used in the biologically relevant dose range), the radiation-altered bases are less studied. Attempts have been made to devise assays for base-damage measurement in cellular DNA after irradiation; the problems of using such assays at reasonable radiation doses are discussed. The alternate approach to measuring yields and chemical identities of damages in cells is extrapolation from model systems. The limitations of extrapolation are considered in the context of the intracellular structures in which DNA exists and the problems in predicting mechanisms of intracellular damage induction. The complexities of damages that could be lethal are considered; "double-strand break" is the generic term for a wide variety of damages, each of which is produced by a similar mechanism. Many of the damages caused by multiple radicals have the potential to be lethal. The current work of the author is outlined along with his attempts to throw light on the topics described above. Some potentially fruitful directions for future research are suggested. These would help to build bridges between studies of the physics of energy deposition and the chemistry of cellular radiation damage and to provide a comprehensive basis for the prediction of the biological effects consequent to the deposition of radiation energy.