I will describe the recent solution (Bryan-Pandharipande) to the local theory of curves. That is, the equivariant Gromov-Witten theory whose target is the total space of a rank two bundle over a curve. This theory turns out to have surprising connections with many other theories from both mathematics and physics. In physics, Aganagic, Ooguri, Saulina, and Vafa have found relations between the local theory of curves and (1) q deformed 2D Yang-Mills theory, (2) Black hole entropy and (3) Chern-Simons theory of circle bundles over a curve. In mathematics, the local theory of curves is equivalent to (1) the equivariant quantum cohomology of the Hilbert scheme of points in the plane (Okounkov-Pandharipande), (2) the equivariant orbifold quantum cohomology of the symmetric product of points in the plane (Bryan-Graber), and conjecturally (3) the equivariant Donaldson-Thomas theory of rank two bundles over a curve. I will describe and explain some of these connections.