In this talk I will review the classical Cauchy problem for Einstein equations. I will explain some of its geometric features and recast the equations as a system of coupled quasilinear transport-elliptic-Maxwell equations. I will present the global-in-time existence conjecture (aka the conjecture of weak cosmic censorship) and how low regularity local existence results (as the celebrated bounded L2 curvature theorem) can be used to get insight on the formation of singularities. I will then review the classical bounded L2 curvature theorem of Klainerman-Rodnianski-Szeftel and present a version generalised to initial data posed on an initial spacelike and an initial characteristic hypersurface that I obtained jointly with Stefan Czimek.