Mathematical modeling combined with nonlinear least-squares curve fitting provides a systematic, objective, reproducible, and consistent method to aid the interpretation of ligand-binding data. It forces the experimentalist to formulate hypotheses in an unambiguous manner and to consider alternative, closely related models as plausible counter-hypotheses. Modeling provides estimates of the "goodness-of-fit" of the theory to the data and estimates of the minimal uncertainty of the parameters. With the availability of many programs for micro- and mini-computers, as well as mainframe computers, these methods are now becoming widely used. Accordingly, we must emphasize a number of potential problems and limitations, based on our experience. Interpretation of results of modeling study should be made, in light of the following points: no amount of computer analysis will compensate for "bad" or insufficient data, or for poor experimental design; the interpretation of the computer analysis is subject to the caveat that all underlying assumptions must be satisfied; one must examine the data graphically in several coordinate systems (e.g., "raw data," as well as standardized residuals); one must continuously search for possible systematic biases or artifacts; one must closely examine the reproducibility of results between multiple experiments; and one must recognize that all of the "test tubes" in an experiment are not necessarily "independent observations" in a statistical sense. In view of these potential problems and limitations, one should always seek to corroborate results and interpretations of "modeling" studies of ligand binding by independent biochemical, biophysical, or structural evidence. In this context, ligand-binding studies, appropriately analyzed, can play a useful and constructive role.