Descriptive and statistical age-period-cohort (APC) analysis methods have received considerable attention in the literature. The statistical modeling of APC data often involves the popular multiple classification model, a model containing the effects of age groups (rows), periods of observation (columns), and birth cohorts (diagonals of the age-by-period table). The identifiability problem inherent to this model is discussed, and its adverse effects on the results of APC modeling exercises are illustrated numerically. Potential problems attendant with the use of two-factor models are described, and other possible modeling approaches currently in use are discussed. Interpretational limitations due to certain innate characteristics of typical APC data sets are also detailed. Given all the documented potential sources for error, the current state-of-the-art regarding the statistical modeling of APC data should be considered to be at an early stage of development.