In this talk, I am going to discuss problems and research regarding Approximate Nearest Neighbor Search in the Recommender Systems. In particular: • The role of fast Approximate Nearest Neighbor search in the multi-stage funnel design or a typical Recommender System. • Research on Approximate Nearest Neighbor search with neural ranking distances and its transformative effects on the end-to-end funnel design. • Existing work on compression-friendly embeddings and parameter tuning.