The goal of this thesis is to give an exposition of the following recent result of Freeman, Lennard, Odell, Turett and Randrianantoanina. A Banach space has the Schur property if and only if every weakly compact set is contained in the closed convex hull of a weakly null sequence. This result complements an old result of Grothendieck (now called the Grothendieck Compactness Principle) stating that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. We include many of the relevant definitions and preliminary results which are required in the proofs of both of these theorems.