An overview Criminology is broadly defined as the making of laws, the breaking of laws, and reacting to the breaking of laws (Sutherland 1947). Historically, criminologists have focused on the second component, the breaking of laws, seeking to understand the causes, motivations, and distribution of criminal behavior. This talk will provide an overview of a dominant area of criminology, the study criminal careers. Why are men and adolescents more prone to be involved in criminal activities? Why do some individuals desist from crime over time while others continue to be involved? Starting with a description of main criminological theories on criminal careers, this talk highlights a controversy in criminology between typological theoretical approaches, a theory of an invariant age-crime curve that is assumed to retain the same shape across all social groups and historical periods, and competing theories of the age-crime relationship. Associated statistical developments are illustrated. Finally, related challenges of measurement, predictive policing and recidivism prediction are briefly described.