  In addition to the well-known Landauer-Buttiker scattering theory and the
nonequilibrium Green's function technique for mesoscopic transports, an
alternative (and very useful) scheme is quantum master equation approach. In
this article, we review the particle-number (n)-resolved master equation (n-ME)
approach and its systematic applications in quantum measurement and quantum
transport problems. The n-ME contains rich dynamical information, allowing
efficient study of topics such as shot noise and full counting statistics
analysis. Moreover, we also review a newly developed master equation approach
(and its n-resolved version) under self-consistent Born approximation. The
application potential of this new approach is critically examined via its
ability to recover the exact results for noninteracting systems under arbitrary
voltage and in presence of strong quantum interference, and the challenging
non-equilibrium Kondo effect.
