Interfaces are essential elements in nanoscale devices and their properties can differ significantly from their bulk counterparts. Because interfaces often act as bottlenecks in heat dissipation, the prediction and control of the interfacial thermal conductance is critical to the design of nanoscale devices. In this review, we examine the recent advances in quantum interfacial thermal transport from a theoretical and computational perspective. We discuss in detail recent advances in the Atomistic Green's Function method which is an important tool for predicting interfacial thermal transport. We also discuss recent progress in the understanding of interfacial transport mechanisms, including the role of interfacial modes, the role of anharmonic phonon-phonon coupling, the role of electron-phonon interaction, and the ways to tune the interfacial thermal conductance. Finally, we give an overview of the challenges and opportunities in this research field.