Abstract: Consider a smooth projective surface S and a sufficiently ample line bundle L. Göttsche’s conjecture states for any r, that the number of r-nodal curves in the linear system |L| is a universal polynomial of Chern numbers of S and L. Göttsche’s conjecture now has several proofs and many generalizations. In this talk, I will explain the generalization of Göttsche’s conjecture for higher dimensional subvarieties with more complicated singularities, the refined curve counting invariants conjectured by Göttsche and Shende, and some computation results.