Abstract: We will begin with the story of homological mirror symmetry of toric varieties. In particular, we will review some definitions from the microlocal theory of sheaves and the coherent-constructible correspondence. For a given toric surface, we are interested in counting nodal curves with fixed intersection points with the boundary divisors. In some examples, we will see how this can be done by looking at the moduli space of certain constructible sheaves on the A-side. This is an ongoing project joint with Eric Zaslow.