I'll explain my recent construction, with Hacking and Gross, of the mirror family to a log Calabi-Yau surface, and some of its many applications both to symplectic topology, and classical algebraic geometry. For example as a corollary of the construction we discover: The complement of a plane cubic has "theta-functions" -- a canonical basis of polynomial functions, analogous to (but considerably rich than) classical theta functions for Abelian varieties, together with a rule for multiplying them determined by counts of plane rational curves meeting the cubic at a single point. We also conjecture that this coordinate ring is the symplectic homology ring of this (open) CY surface, so in particular the symplectic homology has the same theta function structure.