Analysis of thermal systems on the basis of the second law of thermodynamics has recently gained considerable attention. This is, in part, due to the fact that this approach along with the powerful tools of entropy generation and exergy destruction provides a unique method for the analysis of a variety of systems encountered in science and engineering. Further, in recent years there has been a surge of interest in the thermal analysis of conductive media which include solid structures. In this work, the recent advances in the second law analyses of these systems are reviewed with an emphasis on the theoretical and modeling aspects. The effects of including solid components on the entropy generation within different thermal systems are first discussed. The mathematical methods used in this branch of thermodynamics are, then, reviewed. This is followed by the conclusions regarding the existing challenges and opportunities for further research. (C) 2016 Elsevier Ltd. All rights reserved.