Due to the prevelance of fast and slow timescales in enzyme-catalyzed reactions, geometric singular perturbation theory (GSPT) plays a pivotal role in the mathematical illustration of enzyme kinetics. I’ll begin the talk by reviewing some of the earlier work that characterizes single-enzyme/single-substrate (SE/SS) reactions. At the same time, I’ll introduce some of the principal theorems of GSPT and demonstrate their applicability to SE/SS reactions. Finally, I’ll conclude with a description of my current work on coupled reactions. Coupled reactions generally consist of multiple fast timescales and multiple slow timescales; thus, they serve as a novel platform from which to study the applicability of GSPT in higher dimensional dynamical systems.