We present the recent data issued from the Halls A and B of Jefferson Laboratory for the Deep Virtual Compton Scattering Process on the proton. An important set of data for beam spin asymmetries, unpolarized cross sections and differences of polarized cross sections have been obtained. We modestly attempt a first “global” analysis of these three observables at a single <xB>, <Q2> and <−t> kinematic point. We find that it is extremely challenging to describe simultaneously these data in the framework of a few Generalized Parton Distributions models.