Exotic electronic and transport properties of graphene

A brief review is given on electronic and transport properties of monolayer graphene from a theoretical point of view. The topics include the effective-mass description of electronic states, topological anomaly associated with Berry's phase, singular diamagnetic susceptibility, zero-mode anomalies and their removal due to level broadening effects, screening effect and charged impurity scattering, the symmetry crossover among symplectic, unitary, and orthogonal due to the presence of special time reversal symmetry, and anomaly and magnetic oscillation of long-wavelength optical phonons.