Age-period-cohort models have been used to examine and forecast cancer incidence and mortality for over three decades. However, the fitting and interpretation of these models requires great care because of the well-known identifiability problem that exists; given any two of age, period, and cohort, the third is determined. In this paper, we review the identifiability problem and models that have been proposed for analysis, from both frequentist and Bayesian standpoints. A number of recent analyses that use age-period-cohort models are described and critiqued before data on cancer incidence inWashington State are analyzed with various models, including a new Bayesian approach based on an identifiable parameterization. © Institute of Mathematical Statistics, 2016.