This chapter discusses superlative indices, exploring their relationship with the cost-of-living index (COLI) and how they can provide a good approximation without precise knowledge of the utility and expenditure functions. It explains the concept of “exact” indices, such as the Sato–Vartia index, which aligns perfectly with the COLI under specific utility functions like the Constant Elasticity of Substitution (CES). The chapter also introduces the theory of superlative indices, which simplifies the computation of exact indices by using standard indices like Fisher, Walsh, and Törnqvist without identifying the underling expenditure function. Key examples are given to illustrate how these indices correspond to the COLI under various assumptions, showing how superlative indices can be computed easily and how they approximate the true COLI effectively. The discussion highlights their practical significance in simplifying complex economic measurements and their impact on theoretical and practical economics, making them pivotal in modern index number research.