Three-component systems are often more complex than their two-component counterparts. Although the reversible association of three components in solution is critical for a vast array of chemical and biological processes, no general physical picture of such systems has emerged. Here we have developed a general, comprehensive framework for understanding ternary complex equilibria, which relates directly to familiar concepts such as EC50 and IC50 from simpler (binary complex) equilibria. Importantly, application of our model to data from the published literature has enabled us to achieve new insights into complex systems ranging from coagulation to therapeutic dosing regimens for monoclonal antibodies. We also provide an Excel spreadsheet to assist readers in both conceptualizing and applying our models. Overall, our analysis has the potential to render complex three-component systems--which have previously been characterized as "analytically intractable"--readily comprehensible to theoreticians and experimentalists alike.