Since its discovery in 2005, graphene has been the focus of intense theoretical and experimental study owing to its unique two-dimensional band structure and related electronic properties. In this thesis, we explore the electronic properties of graphene structures from several perspectives including the magnetoelectrical transport properties of monolayer graphene, gap engineering and measurements in bilayer graphene, and anomalous quantum oscillation in the monolayer-bilayer graphene hybrids. We also explored the device implications of our findings, and the application of some experimental techniques developed for the graphene work to the study of a complex oxide, Ca3Ru2O7, exhibiting properties of strongly correlated electrons.;Graphene's high mobility and ballistic transport over device length scales, make it suitable for numerous applications. However, two big challenges remain in the way: maintaining high mobility in fabricated devices, and engineering a band gap to make graphene compatible with logical electronics and various optical devices. We address the first challenge by experimentally evaluating mobilities in scalable monolayer graphene-based field effect transistors (FETs) and dielectric-covered Hall bars. We find that the mobility is limited in these devices, and is roughly inversely proportional to doping. By considering interaction of graphene's Dirac fermions with local charged impurities at the interface between graphene and the top-gate dielectric, we find that Coulomb scattering is responsible for degraded mobility.;Even in the cleanest devices, a band gap is still desirable for electronic applications of graphene. We address this challenge by probing the band structure of bilayer graphene, in which a field-tunable energy band gap has been theoretically proposed. We use planar tunneling spectroscopy of exfoliated bilayer graphene flakes demonstrate both measurement and control of the energy band gap. We find that both the Fermi level and electronic structure are highly sensitive to tunnel bias-induced charging in these devices, an effect that is traditionally neglected in other materials. However, careful consideration of both these effects and non-ideal tunneling processes allows extraction of valuable information from the tunneling spectra. We compare the tunable insulating state to our transport studies of bi-layer graphene-based FETs with similar dielectric environments. This work, as well as our work on top-gated monolayer-based devices, identifies the integration of graphene and a gate dielectric as being the next great challenge towards the realization of graphene-based electronics.;We also report the discovery of anomalous quantum oscillations in magnetotransport measurements of monolayer and bilayer graphene hybrids. In these graphene hybrid structures, the Fermi levels of either portion lock at their interface, and the greatly different energy scales of emergent Landau levels support strong charge imbalance. The nature the interface states are yet to be clarified.;Finally, we extend the techniques of device fabrication and measurement to exfoliated flakes of a layered material, Ca3Ru2O 7. This strongly correlated electronic system hosts a variety of exotic phenomena at low temperatures, which have been suggested to result from complex d-orbital interactions. We compare transport measurements of flakes to previous studies in bulk crystals, and explore the effects of tuning charge carrier density using an ionic liquid gate to induce densities several orders of magnitude greater than is possible with conventional dielectrics.
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