Employing the nonequilibrium Green function (NEGF) method at the atomistic level, we study the heat transport in nano-scale systems. Using diagramatic expansions of NEGFs we investigate the effects of anharmonic interactions in quantum thermal transport. The effects of nonlinear interactions on phononic transport are investigated. Specifically, the questions of thermal rectification and negative differential thermal resistance are addressed. Two possible schemes to control thermal rectification are discussed. The first one is by creating a mass gradient along the structure which is achieved experimentally by coating of a nanotube. The second one is modulating the width of the nanostructure along the transport direction which can be realized using graphene nanoribbons or Si nanowires.