Explore the evolution from small-world network phenomena to modern web-scale search algorithms in this research seminar by Microsoft Principal Researcher Ravishankar Krishnaswamy. Discover how vector search and Approximate Nearest Neighbor Search (ANNS) form the backbone of contemporary web search engines, recommendation systems, and generative AI applications that handle billions to trillions of items. Learn about the core principles behind these scalable algorithms, understand the practical challenges of implementing them at web scale, and examine their critical role in enabling today's search and AI-powered systems. Gain insights into the geometric properties of learned representations and how they enable semantic retrieval of related objects. The presentation traces the theoretical foundations from small-world network theory through to the practical algorithms that power modern large-scale information retrieval systems, providing both historical context and current applications in the field of computational search and artificial intelligence.