Age-Period-cohort models are widely used by epidemiologists to analyse trends in disease incidence and mortality. The interpretation of such models is fraught with difficulty in view of the exact linear dependency between the three variables. It is the purpose of this paper to review, compare and contrast some of the more common approaches to this problem based on Poisson regression and a linear model for the log rates. Also the results of using the different approaches on a single series of data on breast cancer incidence among females in Scotland from 1960-1989 are presented for comparison. Recommendations as to the merits and drawbacks of the approaches are also given in the conclusions. Models which are based upon the estimable contrasts such as local curvatures and deviations from linearity are most suitable.