Criminological research has consistently uncovered a positive correlation between past and current criminal behavior. Continuity in offending over time can be attributed to at least two processes-population heterogeneity and state dependence. A population heterogeneity process attributes stability in offending over time to differences in an anti-social characteristic (self-control, impulsivity, psychopathic personality) across persons that is established early in life and time-stable thereafter. An implication of a population heterogeneity explanation for continuity in offending over time is that the anti-social characteristic is likely to have reverberations throughout life, taking many manifestations later in life (unemployment, drug addiction, marital instability). Any observed correlation between these later life events and criminality, therefore, is spurious rather than causal, due to the fact that they are all the effects of a common cause. A state dependence explanation, in contrast, attributes observed stability in criminal offending to a process of contagion. That is, criminal behavior has a genuine causal effect on subsequent criminality by eroding constraints and strengthening incentives to crime. The implication of a state dependence process is that criminal conduct may be influenced by later life events. In this paper, we draw a connection between population heterogeneity and state dependence processes and extant criminological theory. We also review the literature that has investigated the plausibility of these two processes. Finally, concluding that we know very little about them we make recommendations for future research on population heterogeneity and state dependence.