  This review deals with the nonequilibrium Green's function (NEGF) method
applied to the problems of energy transport due to atomic vibrations (phonons),
primarily for small junction systems. We present a pedagogical introduction to
the subject, deriving some of the well-known results such as the Laudauer-like
formula for heat current in ballistic systems. The main aim of the review is to
build the machinery of the method so that it can be applied to other
situations, which are not directly treated here. In addition to the above, we
consider a number of applications of NEGF, not in routine model system
calculations, but in a few new aspects showing the power and usefulness of the
formalism. In particular, we discuss the problems of multiple leads, coupled
left-right-lead system, and system without a center. We also apply the method
to the problem of full counting statistics. In the case of nonlinear systems,
we make general comments on the thermal expansion effect, phonon relaxation
time, and a certain class of mean-field approximations. Lastly, we examine the
relationship between NEGF, reduced density matrix, and master equation
approaches to thermal transport.
