Elliptic surfaces are ubiquitous in Mathematics. Examples include Enriques surfaces, Dolgachev surfaces, all surfaces of Kodaira dimension one, and many rational surfaces. In this talk we will focus on the latter. It is a classical result that all rational elliptic surfaces can be realized as a nine-fold blow-up of the plane, where the nine points (possibly infinitely near) are the base points of a pencil of plane curves of degree 3m, each of multiplicity m. The number m is called the index of the fibration. In joint work with Rick Miranda we have constructed a moduli space for rational elliptic surfaces of index two as a toric GIT quotient. The goal of my talk will be to explain our construction.