The criminal careers approach emphasizes a potential heterogeneity of offending groups in the general population. This model leads to a distinction between the incidence and prevalence of criminal offending; a focus on the onset, persistence, and cessation of criminal careers; and the possibility that criminals are a distinctive group with constant high rates of offending. In contrast, the life course approach emphasizes a potential heterogeneity of offenders with respect to the order of criminal events from first order to second order to higher order. This approach suggests an analysis of risks or hazards of offending by order of offense. The use of semiparametric mixed Poisson regression techniques demonstrates the complementarity of the two approaches, even though each approach has a different focus. Tables, figures, footnotes, and 50 references (Author abstract modified)