We study geometric Entanglement Entropy in AdS/CFT. A way to compute Entanglement Entropy in AdS/CFT bas been conjectured by Ryu and Takayanagi (RT). The conjecture has provided extensive and valuable insight into the strong coupling dynamics of certain quantum field theories. However it remains unproven within the usual rules of AdS/CFT. We discuss efforts to prove the formula for some of the simplest non-trivial cases. This involves the construction of Holographic Entanglement Renyi Entropies as an intermediate step. Under certain assumptions we can reproduce the predictions of RT. Our work gives insights into the inner workings of the RT formula and paves the way to understanding various corrections to the formula when going beyond classical gravity - a necessary step in applying holography to more realistic theories.