Interfacial thermal resistance also known as Kapitza resistance continues to be poorly understood thermal transport phenomena despite longstanding efforts to elucidate, predict and ultimately control its magnitude in the technologically important systems. Relevant examples include thermoelectrics, where the best figure of merit is achieved for the superlattice, and high power electronics, where efficient heat removal from the individual components is severely diminished by the interfacial resistance. Notice that in the first instance Kapitza resistance need to be maximized, while in the other it has to be minimized. In addition, grain boundaries significantly affect thermal transport in nanocrystalline materials which are found more and more applications. In this presentation, basics of the thermal boundary resistance will be reviewed along with the computational methodology necessary to simulate it using atomistic simulations. Particular attention will be paid the techniques that deliver spectral information about the boundary resistance. Further, specific examples will be discussed which include grain boundary resistance in technologically important oxides.