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We aim to provide engineers with an introduction to the nonequilibrium Green's function (NEGF) approach, which is a powerful conceptual tool and a practical analysis method to treat nanoscale electronic devices with quantum mechanical and atomistic effects. We first review the basis for the traditional, semiclassical description of carriers that has served device engineers for more than 50 years. We then describe why this traditional approach loses validity at the nanoscale. Next, we describe semiclassical ballistic transport and the Landauer-Buttiker approach to phase-coherent quantum transport. Realistic devices include interactions that break quantum mechanical phase and also cause energy relaxation. As a result, transport in nanodevices is between diffusive and phase coherent. We introduce the NEGF approach, which can be used to model devices all the way from ballistic to diffusive limits. This is followed by a summary of equations that are used to model a large class of structures such as nanotransistors, carbon nanotubes, and nanowires. Applications of the NEGF method in the ballistic and scattering limits to silicon nanotransistors are discussed.