Inspired by earlier work of Okounkov, Lazarsfeld and Mustata introduced a construction recently, which associates a convex body in R^n to a big divisor on an n-dimensional projective variety. This viewpoint renders many properties of volumes more transparent, and has since been used to study arithmetic analogue of big line bundles. In this talk I will begin by introducing Lazarsfeld and Mustata's construction, and then go on to explain my work on these bodies which shows that they encode all numerical invariants of a big divisor.