Abstract: The deep connection between enumerative geometry and integrable hierarchies has been fascinating since early 1990s. In this talk we address our recent progress on two questions: whether an enumerative geometry theory is related to KP-type hierarchy; how to locate such a theory inside the space of KP/BKP hierarchies. Both answers lead to the structure of an underlying Riemann surface, in the sense of “classical” and “quantum” respectively.