The intense interest in 'offender profiling' generated by FBI special agents, gave rise to an explosion of studies in a new area called 'investigative psychology' by its originator David Canter. This develops understanding of offenders' behaviour that can be harnessed to improve investigations. In this rapidly developing area much has been learnt about what offenders reveal about themselves through their styles of offending. Beyond criminals' actions the location of their crimes can also reveal where the offender lives or which offences can be linked as part of the same series. Investigative psychologists also explore how to interview witnesses and suspects and assess the veracity of accounts given. The variation in criminal style across crimes as diverse as arson, burglary, hostage negotiation, serial killing and sexual assault is reviewed, using narrative theory and criminals' emotional experience when offending as the basis for explaining these variations. This provides a framework for drawing inferences about offenders' characteristics. Studies in investigative psychology require a special methodology, developed by David Canter to allow scientific explorations in such a challenging field, previously assumed not to be open empirical study. The practical potential and applications of the research are given, as well as a selection of commentaries on the cutting edge debates that are driving the future of the investigative psychology. This new discipline is of relevance to forensic psychologists in many different settings, criminologists and law enforcement agencies, bringing together work that lays out current achievements and sets the agenda for future research in the field.