Purpose. The psychological hypotheses that form the foundations for ‘Offender Profiling’ are identified and the research that has tested them is reviewed. Argument. ‘Offender profiling’ is taken to be the derivation of inferences about acriminal from aspects of the crime(s) he or she has committed. For this process to move beyond deduction based on personal opinion and anecdote to an empirically based science, a number of aspects of criminal activity need to be distinguished and examined. The notion of a hierarchy of criminal differentiation is introduced to highlight the need to search for consistencies and variations at many levels of that hierarchy. However, current research indicates that the key distinctions are those that differentiate, within classes of crime, between offences and between offenders. This also leads to the hypothesis ofa circular ordering of criminal actions, analogous to the colour circle, a ‘radex’. The radex model, tested using Multi‐Dimensional Scaling (MDS) procedures, allows specific hypotheses to be developed about important constituents of criminal differentiation: Salience. MDS analyses reveal the importance of the frequency of criminal actions as the basis on which the significance of those actions can be established. Models of differentiation. The research reviewed mainly supports distinctions between criminals in terms of the forms of their transactions with their explicit or implicit victims. Consistency. Offenders have been shown to exhibit similar patterns of action on different occasions. The most reliable examples of this currently are in studies of the spatial behaviour of criminals. Inference. Under limited conditions it is possible to show associations between the characteristics of offenders and the thematic focus of their crimes. In general these results provide support for models of thematic consistency that link the dominant themes in an offender's crimes to characteristic aspects of his or her lifestyle and offending history. Implications. Much of what passes for ‘o...