A clear understanding and proper control of interfacial thermal transport is important in nanoscale devices.In this review,we first discuss the theoretical methods to handle the interfacial thermal transport problem,such as the macroscopic model,molecular dynamics,lattice dynamics,and quantum transport theories.Then we discuss various effects that can significantly affect the interfacial thermal transport,such as the formation of chemical bonds at interface,defects,interface roughness,strain,substrates,atomic species,mass ratios,and structural orientations.Then importantly,we analyze the role of inelastic scattering at the interface,and discuss its application in thermal rectifications.Finally,the challenges and promising directions are discussed.