This chapter explores the difficulties and methodologies associated with constructing price indices when the set of goods changes over time. It acknowledges that no two products are “exactly” identical, even within the same category, and the emergence and disappearance of goods complicate price comparisons. Seasonal goods, technological innovations, and disruptions like the COVID-19 pandemic further challenge traditional price measurement methods. The chapter discusses the hedonic method, which adjusts for quality differences by considering various attributes of goods, and highlights its limitations, including the difficulty of measuring new attributes and dealing with multicollinearity. The matching method, which compares only concurrently available goods, is straightforward but prone to bias due to non-random product exits and introductions. The chapter also introduces the concept of variety effects, where changes in the variety of goods impact consumer welfare and the cost-of-living index (COLI). Feenstra’s COLI, which incorporates variety effects, is widely used but can exhibit significant chain drift over time, complicating long-term price comparisons. The chapter concludes by highlighting the ongoing research and practical issues in addressing these challenges, emphasizing the need for innovative approaches and new methodologies.