Refinery complexity quantifies the complexity and sophistication of a refinery and has found widespread application. This chapter describes the main applications and new developments in refining complexity. Complexity indices are frequently used in sales price and replacement cost models in appraisals, and derived measures are frequently used in valuation studies. The complexity factor functional is a two-dimensional function of the capacities of process units. Its functional average values are about 10% larger than complexity factors computed at reference capacity due in part to the larger variable domain. Cost curves are the primary element in the reference capacity and complexity factor functional approaches, while in the traditional approach the complexity factor is computed directly from the raw data. Capacity, complexity, complexity-barrels and replacement cost new are the most common descriptors in sales price models. The chapter concludes by solving an inverse problem that allows complexity factors for process units to be inferred from the complexity indices of a sample of refineries.