Polysaccharide depolymerization in nature is primarily accomplished by processive glycoside hydrolases (GHs), which abstract single carbohydrate chains from polymer crystals and cleave glycosidic linkages without dissociating after each catalytic event. Understanding the molecular-level features and structural aspects of processivity is of importance due to the prevalence of processive GHs in biomass-degrading enzyme cocktails. Here, we describe recent advances towards the development of a molecular-level theory of processivity for cellulolytic and chitinolytic enzymes, including the development of novel methods for measuring rates of key steps in processive action and insights gained from structural and computational studies. Overall, we present a framework for developing structure-function relationships in processive GHs and outline additional progress towards developing a fundamental understanding of these industrially important enzymes.