Backcalculations is an important method for reconstructing past rates of human immunodeficiency virus (HIV) infection and for estimating current prevalence of HIV infection and future incidence of acquired immunodeficiency syndrome (AIDS). This paper reviews the backcalculation technique, focusing on the key assumptions of the method, including the necessary information regarding incubation, reporting delay, and models for the infection curve. A summary is given of the extend to which the appropriate external information is available and whether checks of the relevant assumptions are possible through use of data on AIDS incidence from surveillance systems. A likelihood approach to backcalculation is described and implemented on AIDS incidence data in the United States. New features of the approach influence incorporation of seasonal variation in diagnosis rates, smooth nonparametric estimation of both the HIV infection curve and nonstationary aspects of the incubation period and reporting delay distributions, and an analysis of residuals from backcalculation fits. Unexplained lack of fit is examined and discussed. A fundamental concern is the appropriate acknowledgment of uncertainty associated with backcalculation estimates caused by misspecified assumptions and inaccurate external estimates of key components of the technique. Such uncertainty limits the usefulness of backcalculation and highlights the need for complementary approaches.