Ionizing radiation causes both singly and multiply damaged sites in DNA when the range of radical migration is limited by the presence of hydroxyl radical scavengers (e.g. within cells). Multiply damaged sites are considered to be more biologically relevant because of the challenges they present to cellular repair mechanisms. These sites occur in the form of DNA double-strand breaks (dsb) but also as other multiple damages that can be converted to dsb during attempted repair. The presence of a dsb can lead to loss of base sequence information and/or can permit the two ends of a break to separate and rejoin with the wrong partner. (Multiply damaged sites may also be the biologically relevant type of damage caused by other agents, such as UVA, B and/or C light, and some antitumour antibiotics.) The quantitative data available from radiation studies of DNA are shown to support the proposed mechanisms for the production of complex damage in cellular DNA, i.e. via scavengable and non-scavengable mechanisms. The yields of complex damages can in turn be used to support the conclusion that cellular mutations are a consequence of the presence of these damages within a gene. Literature data are used to support these statements and to develop overall mechanisms connecting the production of primary species to the production of biologically relevant damages. The consequences of the LET of the radiation on multiplicity of damage are discussed and suggestions made for the cause of the decrease of the oxygen enhancement ratio as the LET increases.