Some authors advocate artificial neural networks as a replacement for statistical forecasting and decision models; other authors are concerned that artificial neural networks might be oversold or just a fad. In this paper we review the literature comparing artificial neural networks and statistical models, particularly in regression-based forecasting, time series forecasting, and decision making. Our intention is to give a balanced assessment of the potential of artificial neural networks for forecasting and decision making models. We survey the literature and summarize several studies we have performed. Overall, the empirical studies find artificial neural networks comparable with their statistical counterparts. We note the need to consider the many mathematical proofs underlying artificial neural networks to determine the best conditions for their use in forecasting and decision making.