The problem of solving the hydrodynamics of a strongly-coupled relativistic expanding fluid is addressed using the AdS/CFT correspondence. We use the Gauge/Gravity duality as a theoretical laboratory (in N=4 supersymmetric gauge theories) for what could be relevant for an expanding quark-gluon plasma formed during heavy-ion collisions. The perfect-fluid behaviour at large proper-times, the calculation of viscosity of the moving plasma, the problem of short thermalization times, the inclusion of flavor, the study of plasma instabilities and other issues, appear to be related to non-trivial properties of a moving Black Hole geometry which arises from the Gauge/Gravity correspondence using holomorphic renormalization. Work in progress and open problems will be discussed.