  Given a singular variety I discuss the relations between quantum cohomology
of its resolution and smoothing. In particular, I explain how toric
degenerations helps with computing Gromov--Witten invariants, and the role of
this story in Fanosearch programme. The challenge is to formulate enumerative
symplectic geometry of complex $3$-folds in a way suitable for extracting
invariants under blowups, contractions, and transitions.
