In this talk I will describe a new and surprising connection between refined BPS states and Ramanujan's mock modular forms. On the physics side, the connection involves a system that provides a home to homological knot invariants and categorification of quantum groups, which led to many concrete and surprising predictions. Relation to mock modular forms is yet another such prediction, that one finds in categorification of RTW invariants of 3-manifolds. The relation between refined BPS invariants and mock modular forms can be formulated in many equivalent ways: via enumerative geometry of Calabi--Yau 3-folds, via 3d-3d correspondence,via 2d Landau--Ginzburg theory, etc. It would be interesting to see if there is any connection to a similar relation between mock modular forms and BPS states in the context of umbral moonshine and black hole microstate counting. This talk is based on the recent work with P.Putrov and C.Vafa.