Nearly four generations of investigators have studied combined drug effects. Their methods of generating and analyzing data have changed dramatically over the years but the basic problem has not. This review examines the inherent difficulties in analyzing combined drug effects and evaluates modern methods of describing these interactions. Researchers have traditionally used two-dimensional (2-D) methods to approximate the actual three-dimensional (3-D) nature of drug interactions. We conclude that these 2-D methods are often inadequate when used to analyze synergistic and antagonistic drug interactions in antiviral and anticancer chemotherapy. We propose a direct and pragmatic 3-D approach to the problem, made possible by microcomputers and sophisticated graphics programs. This procedure directly elucidates the shape of the dose-response surface, identifies the regions of statistically significant synergy and antagonism, and quantitates these effects. It also greatly simplifies the problem since a 3-D surface presents complete drug interactions in a way that can be easily interpreted. We will show that understanding the shape of the resulting 3-D surface is essential to an understanding of complex drug interactions. This new method facilitates the rigorous analysis of drug-drug interactions and offers investigators powerful new tools to analyze combinations of antiviral and anticancer drugs.