  Understanding the electronic and phononic transport properties of junctions
consisting of a scattering region such as a nanoscale matters or molecules
connected to two or more electrodes is the central basis for future nano and
molecular scale applications. The theoretical and mathematical techniques to
treat electron and phonon transport are leading to model the physical
properties of nano and molecular scale junctions. My aim in this paper is to
review the theoretical and mathematical techniques to treat electron and phonon
transport in nano and molecular scale junctions leading to models of their
physical properties. This helps not only to understand the experimental
observations but also provides a vital design tool to develop strategies for
molecular electronic building blocks, thermoelectric device and sensors.
