  In this colloquia review we discuss methods for thermal transport
calculations for nanojunctions connected to two semi-infinite leads served as
heat-baths. Our emphases are on fundamental quantum theory and atomistic
models. We begin with an introduction of the Landauer formula for ballistic
thermal transport and give its derivation from scattering wave point of view.
Several methods (scattering boundary condition, mode-matching, Piccard and
Caroli formulas) of calculating the phonon transmission coefficients are given.
The nonequilibrium Green's function (NEGF) method is reviewed and the Caroli
formula is derived. We also give iterative methods and an algorithm based on a
generalized eigenvalue problem for the calculation of surface Green's
functions, which are starting point for an NEGF calculation. A systematic
exposition for the NEGF method is presented, starting with the fundamental
definitions of the Green's functions, and ending with equations of motion for
the contour ordered Green's functions and Feynman diagrammatic expansion. In
the later part, we discuss the treatments of nonlinear effects in heat
conduction, including a phenomenological expression for the transmission, NEGF
for phonon-phonon interactions, molecular dynamics (generalized Langevin) with
quantum heat-baths, and electron-phonon interactions. Some new results are also
shown. We also briefly review the experimental status of the thermal transport
measurements in nanostructures.
