Societies' increasing need for energy storage makes it necessary to explore new concepts beyond the traditional lithium ion battery. A promising candidate is the lithium-sulfur technology with the potential to increase the energy density of the battery by a factor of 3-5. However, so far the many problems with the lithium-sulfur system have not been solved satisfactory. Here we report on a new approach utilizing a self-standing reduced graphene oxide based aerogel directly as electrodes, i.e. without further processing and without the addition of binder or conducting agents. We can thereby disrupt the common paradigm of "no battery without binder" and can pave the way to a lithium-sulfur battery with a high practical energy density. The aerogels are synthesized via a one-pot method and consist of more than 2/3 sulfur, contained inside a porous few-layered reduced graphene oxide matrix. By combining the graphene-based aerogel cathode with an electrolyte and a lithium metal anode, we demonstrate a lithium-sulfur cell with high areal capacity (more than 3 mAh/cm2 after 75 cycles), excellent capacity retention over 200 cycles and good sulfur utilization. Based on this performance we estimate that the energy density of this concept-cell can significantly exceed the Department of Energy (DEO) 2020-target set for transport applications.