This article reviews the commonly used methods for representing electronic potential-energy surfaces for small molecules and simple chemical reactions in terms of globally defined analytical functions. Four classes of methods are discussed: spline fitting methods, semiempirical methods, many-body expansion methods, and methods that represent global surfaces based on information determined along reaction paths. The application of these methods is examined in detail for four triatomic systems and one four-atom system: $\mathrm{O}\left({}_{}{}^3{}_{}{}^{}P\right)+{\mathrm{H}}_2$, Cl+HCl, H+CO, $\mathrm{O}\left({}_{}{}^1{}_{}{}^{}D\right)+{\mathrm{H}}_2\to {\mathrm{H}}_2\mathrm{O}\to \mathrm{OH}+\mathrm{H}$, and H+C${\mathrm{O}}_2$→OH+CO. These examples illustrate both the art and the pitfalls of representing surfaces. In addition, the consequences of different potential surface representations for the dynamics of collisions on these surfaces are discussed at length.

DOI:https://doi.org/10.1103/RevModPhys.61.669