We consider the application of high-throughput experimentation (HTE), including combinatorial methods, to catalyst discovery and early-phase optimization. While combinatorial- and parallel-testing methods have an already substantial history in catalysis, recent work by several groups promises significant efficiency gains. In molecular catalysis, progress is noted in library design, library synthesis by pooled, parallel, and discrete formats, catalyst testing and reaction optimization; the prime constraint for organometallic catalysts is the limited scope of synthesis procedures for nonpeptide-based ligand libraries. Routes described for the synthesis of heterogeneous catalysts include hydrothermal synthesis, arraying of solution precursors, automated impregnation and precipitation, and arraying of solid precursors. The key challenge in applying HTE to heterogeneous catalysis is testing; we distinguish here between Stage 1, or "discovery" testing and Stage 2, optimization testing, and describe techniques with potential in each case. Recent examples from the literature and our own work are used to illustrate these principles and the prospects for HTE applied to catalysis.