We critically address the problem of predicting the thermal boundary resistance at the interface between two semiconductors by atomistic simulations. After reviewing the available models, lattice dynamics calculations and molecular dynamics simulation protocols, we reformulate this problem in the language of non-equilibrium thermodynamics, providing an elegant, robust and valuable theoretical framework for the direct calculation of the thermal boundary resistance through molecular dynamics simulations. The foundation of the method, as well as its subtleties and the details of its actual implementation are presented. Finally, the Si/Ge interface showcase is discussed as the prototypical example of semiconductor heterojunction whose thermal properties are paramount in many front-edge nanotechnologies.