In the past six years, several efforts have been directed towards developing a dictionary in between the physics of six-dimesional theories and the algebraic geometry of elliptically-fibered Calabi-Yau three-folds, building upon methods in string theory. This has lead to novel results in enumerative geometry as well, in particular, the Gopakumar-Vafa invariants of the topological string of such Calabi-Yau varieties translate to an operator counting in the six-dimensional theory. This gives an unorthodox perspective on topological strings, unveiling novel modular properties and a connection to Weyl invariant Jacobi forms. This connection follows from six-dimensional physics and can be ultimately traced back to the BPS strings subsector of these models. In this talk we are going to discuss certain aspects and applications of this correspondence, as well as its interplay with recent results about universal features of the BPS strings.