I will present a recent result about an improved region for local existence of vacuum-solutions to the Characteristic Initial Value Problem in General Relativity by Johnathan Luk (2018). I'll start by going through the general setup such as the double-null foliation, the harmonic gauge and talk about the structure of the equations that result from this choice of coordinate system. I'll also briefly recall the Theorem of Rendall, which is the result that is improved here and which acts as a basis for the work from Luk. In the end I'll talk about the difficulties that are present when trying to improve the region of existence and outline the structure as well as the main ideas of the proof.