Vector similarity search is behind every recommendation engine, image lookup, and semantic search you use. But scaling it to billions of vectors with millisecond latency requires clever data structures. In this episode, Lucas and Luna explore Hierarchical Navigable Small World (HNSW) graphs—the algorithm that one startup, Vectara, uses to deliver sub-10ms search on 10 billion vectors. They break down how HNSW works, why it beats brute-force and tree-based methods, and the memory trade-offs involved. Along the way, they discuss the rise of vector databases, the role of approximate nearest neighbor search in modern AI pipelines, and why HNSW has become the de facto standard for production systems. Whether you're building a recommendation engine, a chatbot, or a visual search tool, understanding HNSW will change how you think about high-dimensional data.