An effective approach of quantum transport of Dirac carriers in mono- and bi-layer graphene structures and devices is presented. Initially based on the Green's function formalism to treat the Dirac Hamiltonian of massless particles in two-dimensional mono-layer graphene, the model has been extended to to small bandgap materials and to bi-layer graphene with massive carriers. It is applied to investigate some transport problems as the minimum conductivity, the tunneling properties the spin-polarized transport through single-barrier structures, and the operation of graphene field-effect transistors.