Criminological theorists and criminal justice policy makers place a great deal of importance on the idea of desistance. In general terms, criminal desistance refers to a cessation of offending activity among those who have offended in the past. Some significant challenges await those who would estimate the relative size of the desisting population or attempt to identify factors that predict membership in that population. In this paper, we consider several different analytic frameworks that represent an array of plausible definitions. We then illustrate some of our ideas with an empirical example from the 1958 Philadelphia Birth Cohort Study.