||This thesis focuses on the transport properties of graphene, a new emerging atomically thin, two-dimensional material, with and without the application of a magnetic field. Because of its high mobility, graphene is a promising candidate for Extraordinary Magnetoresistance (EMR) devices. The magnetoresistance of an EMR device arises mainly from its geometry rather than the intrinsic response of the material itself to an applied magnetic field. As a result, the geometric parameters play an important role in its performance. Experiments employing various combinations of geometric parameters and graphene of different quality levels were conducted to determine the optimal results. We found that the optimized parameters vary for different applied magnetic fields. In a magnetic field of 9 Tesla, magnetoresistance up to 55,000% was observed. In addition, Finite Element Analysis (FEA) simulations are used to complement the experiments and explain the measured magnetoresistance. The excellent agreement between the simulations and experimental results indicates that theoretical simulation can be used as a convenient method to explore EMR devices with alternative geometries or materials. The anomalous quantum Hall effect is one of the most exciting properties of graphene. The observation of the v=0 state above a critical magnetic field is closely related to the quality of the graphene, where a higher quality reduces the critical field needed. With our high quality graphene sample, the critical field is reduced to 6.75 Tesla. Moreover, from 6.75 T to 9T, the resistance at the cross point of the metal-insulator transition (MIT) is very close to h/2e2, which resembles the case of a disordered two-dimensional electron gas (2DEG) and may indicate a similar physical mechanism. In addition to the magnetotransport measurements, the current saturation of graphene in a high electric field is studied both theoretically and experimentally. This thesis focuses primarily on bilayer graphene because of the scarcity of research in this area. For the theoretical part, two models are studied in detail and compared with each other. The phonon spontaneous model is analytical and easy to use while the Boltzmann transport method (BET) with shifted Fermi distribution is more complicated. However, this latter method can provide more information before current saturation. The two models are extended to the case of bilayer graphene. For samples with relatively high carrier density, they agree with each other qualitatively. However, in the low carrier density region, the BET method gave a much lower drift velocity, which was explained by the much larger effective charge carrier density, including additional electrons tunneling from the valence band and holes in the valence band. In experiments of bilayer graphene in a high electric field, the carrier drift velocity has been observed to be comparable or even larger than that in monolayer graphene. This was beyond our expectation because monolayer graphene usually displays a much higher low field mobility. Finally, a simple drying method that takes advantage of capillary force is used to create strain in the graphene films, which can be treated as a pseudo-magnetic field. Uniform and non-uniform distribution of strain up to 0.47 percent has been obtained in different geometric devices. With cleaner surfaces between the graphene and underlying substrate, the van der Waals force increases remarkably, and thus, the strain in graphene may be further enhanced.