Computational approaches have made significant contributions to our understanding of heterogeneous catalysis in recent decades. These types of computations have most often been applied for metal-only catalysts, and have made clear that their single-component nature severely limits the extent to which their performance can be improved. In this dissertation, I discuss how I have applied computational modeling to understand and design two types of multi-component catalytic systems: (1) oxide-supported metal catalysts, and (2) plasma-enhanced catalytic systems. I show that both approaches to multi-functionalization provide potential for significant improvement over their single-component counterparts.For the work on metal/support interfaces, I identify several ways by which the support modifies reactivity at the interface, e.g. charge transfer, strain, ligand, and steric effects. All of these effects are potentially tunable---the work provides guidelines on how the metal/support synergy may be exploited to develop superior catalysts. I also discuss the formulations of an initial theory of plasma-enhanced catalysis. I take a reductionist approach to reduce the complexity that hinders an insight-driven approach to the field. I only focus on the potential of the plasma to assist the catalysis by non-thermally activating strong chemical bonds. I show that plasma-driven catalysis can provide access to reaction rates as well as product yields far greater than those accessible thermally at equivalent conditions of bulk temperature and pressure. The simple conceptual framework developed in this thesis helps interpret some of the singular characteristics of plasma-catalysis experiment, as well as to identify materials and operation conditions where the plasma-catalyst coupling may be beneficial. The concepts are applied in the context of the ammonia synthesis and methane reforming reactions.