A comprehensive survey of the evolution of market design over the past three decades. In the mid-1990s, the first Federal Communications Commission spectrum auction and the redesign of the National Residency Matching Program collectively helped to jumpstart the field of market design. Since then, extensive research has improved auction design and broken new conceptual ground in addressing multi-agent matching problems. This volume summarizes key discoveries and advances in market design over the past three decades and explores contemporary challenges--from climate policy and electricity markets to AI-mediated exchanges and hospital resource allocation. Contributors examine how to design efficient, incentive-compatible mechanisms that are robust to shifting conditions and increasing complexity. They consider a wide variety of applications that could benefit from the market design viewpoint, such as environmental markets, school choice, and organ exchange. Together, the chapters illustrate the important interactions between economic theory, computational tools, and institutional insight.