Based on density functional theory and Wannier function bases, topological behaviors of novel materials are studied, including Berry curvature, Chern number, and Hall conductivity etc. Some nontrivial topological states, such as quantum anomalous Hall effects (QAHE), valley Hall states (VHS), and valley-polarized metallic states (VPMS), are predicted. We also study the effects of spin-orbit coupling (SOC) in spintronics, including spin polarization, spin Hall Effect, and spin current. A numerical method was developed to deal with spin transport of SOC sample with boundaries and interfaces. For quantum transport in nanostructures, the problems studied contain I-V characteristics, local heating, current-induced forces, and shot noise in quantum-point contacts. The electronic transport properties in currently hot materials of graphene are studied.