This dissertation contains several enzyme kinetics studies, each demonstrating the importance of dimensional analysis in justifying rate expressions and the usefulness of perturbation techniques in generating approximate time-dependent solutions. Our focus has been on the action of cellulases, enzymes which hydrolyze the glycosidic bonds of cellulose, releasing sugars which can be used as feedstock for renewable commodities and fuels. The process involves two fundamental steps at the solid-liquid phase boundary: enzyme binding and hydrolysis. The development of detailed mathematical models plays an essential role in understanding the mechanism of this heterogeneous process. First, we present two homogenous enzyme kinetics studies, where reactions are carried out in a single well-mixed liquid-phase. The first study focuses on the Michaelis-Menten (MM) mechanism for enzyme kinetics. The mass balances for MM kinetics are simple to write but deceptively difficult to solve; consequently, various approximate solutions have been offered over the past 50 years, none of which works in all cases. We generate a uniformly-valid time-dependent solution that converges accurately for any combination of initial conditions, and we systematically define where each previous solution fits within the new solution. In the second study, we investigate the hydrolysis of p-nitrophenyl cellobioside by Thermobifida fusca Cel5A, a retaining endocellulase, and develop a mechanistic model for its hydrolysis and transglycosylation in the enzyme's active site. Our work extends previous treatments by providing criteria that justify the use of the quasi-steady-state approximation (QSSA) and provide an integrated form of the resulting rate expression. The results can be extended to other retaining glycosyl hydrolases acting on nitrophenol glycosides. Next, we present a heterogeneous two-phase kinetics model for the hydrolysis of dense cellulose fibers by cellulase enzymes. The model reveals that the shapes of the time-dependent liquid phase concentration curves can appear nearly identical even when different underlying mechanisms are dominant. The results substantiate the importance of including penetration and local reaction history in cellulase kinetics models and of more carefully measuring the evolving shapes of fibers when applying such models. Finally, we review our collaborative efforts to develop a synthetic cellulose substrate with controlled microstructure and physical properties.