The article's aim is to evaluate the application of the evolutionary principles of kin selection, reproductive value, and resource holding power to the understanding of family violence. The principles are described in relation to specific predictions and the mechanisms underlying these. Predictions are evaluated for physical violence perpetrated by (a) parents to unrelated children, (b) parents to genetic offspring, and (c) offspring to parents and between (d) siblings and (e) sexual partners. Precise figures for risks have been calculated where possible. The major conclusions are that most of the evidence is consistent with evolutionary predictions derived from kin selection and reproductive value: There were (a) higher rates of violence to stepchildren, (b) a decline in violence with the age of offspring, and (c) an increase in violence with parental age, while (d) violence between siblings was generally at a low level and concerned resource disputes. The issue of distinguishing evolutionary from alternative explanations is addressed throughout and is problematic for predictions derived from reproductive value. The main evolutionary explanation for male partner violence, mate guarding as a result of paternity uncertainty, cannot explain Western studies where sex differences in control and violence between partners were absent, although other aspects of male partner violence are consistent with it, and it may explain sex differences in traditional cultures. Recurrent problems in evaluating the evidence were to control for possible confounds and thus to distinguish evolutionary from alternative explanations. Suggestions are outlined to address this and other issues arising from the review. (Contains 13 tables, 1 figure and 4 footnotes.)