The fundamental underpinnings of the Gibbs adsorption equation (GAE) are enunciated including sundry choices for the location of the zero-volume dividing surface. Comparison is made to the finite-volume thermodynamic analyses of Guggenheim and Hansen. Provided that Gibbs phase rule is properly invoked, only invariant surface properties appear in the GAE. In the framework of invariant surface properties, both the zero-volume (Gibbs) and the finite-volume (Guggenheim) treatments of the surface phase give identical results for the GAE, confirming the thermodynamic generality and rigor of the expression. Application of the GAE is made to strong and weak electrolytes, to electrified interfaces (Lippmann equation), and to surface complexation. Usefulness of the GAE in molecular simulation of interfaces is outlined. Special attention is paid to the seminal contributions of Fainerman and Miller in applying molecular-thermodynamic interfacial-layer models toward predicting adsorption behavior at fluid/fluid interfaces. Conversion of adsorption isotherms into two-dimensional interfacial-tension equations of state via the GAE is highlighted. Confusion over interpretation of the Gibbs adsorption equation arises primarily because of imprecise meaning for adsorbed amounts. Once invariant adsorptions are recognized and utilized, the Gibbs adsorption equation yields identical results for Gibbs zero-volume surface thermodynamics and for Guggenheim finite-volume surface thermodynamics.