The steady-state quantum transport through a mesoscopic system is discussed. We sart from a simple scattering model of the particles tunnelling through a rectangular barrier. Then the Landauer formula for the tight-binding electronic Hamiltonian is derived for the electronic and heat fluxes. This is followed by the practical aspects of implementing this approach, such as the non-orthogonal basis set, self-consistency and how to account for the leads, including the wide-band approximation. Next we consider inclusion of the electron–electron and electron–phonon interactions to go beyond the Landauer current formula. The phonon heat flux is studied for the harmonic Hamiltonian and the corresponding Landauer formula derived. After that an anharmonic central region is considered and the heat flux through it discussed.