Two graphene layers placed in close proximity offer a unique system to investigate interacting electron physics as well as to test novel electronic device concepts. In this system, the interlayer spacing can be reduced to value much smaller than that achievable in semiconductor heterostructures, and the zero energy band-gap allows the realization of coupled hole-hole, electron-hole, and electron-electron two-dimensional systems in the same sample. Leveraging the fabrication technique and electron transport study in dual-gated graphene field-effect transistors, we realize independently contacted graphene double layers separated by an ultra-thin dielectric. We probe the resistance and density of each layer, and quantitatively explain their dependence on the backgate and interlayer bias. We experimentally measure the Coulomb drag between the two graphene layers for the first time, by flowing current in one layer and measuring the voltage drop in the opposite layer. The drag resistivity gauges the momentum transfer between the two layers, which, in turn, probes the interlayer electron-electron scattering rate. The temperature dependence of the Coulomb drag above temperatures of 50 K reveals that the ground state in each layer is a Fermi liquid. Below 50 K we observe mesoscopic fluctuations of the drag resistivity, as a result of the interplay between coherent intralayer transport and interlayer interaction. In addition, we develop a technique to directly measure the Fermi energy in an electron system as a function of carrier density using double layer structure. We demonstrate this method in the double layer graphene structure and probe the Fermi energy in graphene both at zero and in high magnetic fields. Last, we realize dual-gated bilayer graphene devices, where we investigate quantum Hall effects at zero energy as a function of transverse electric field and perpendicular magnetic field. Here we observe a development of v = 0 quantum Hall state at large electric fields and in high magnetic fields, which is explained by broken spin and valley spin symmetry in the zero energy Landau levels. / text