In this chapter we consider the thermodynamic optimization of thermal insulation systems, i.e., systems designed to maintain a temperature difference between a certain space (hot or cold) and the ambient temperature. This topic is of pivotal importance for the entire field of engineering thermodynamics for two reasons. First, all power plants (e.g., Problem 2.2) and refrigeration plants (e.g., Problem 1.3) function as thermal insulations. The performance of each plant in this huge class of applications can be improved by minimizing the generation of entropy associated with the insulation. The second reason is that the history (chronology) of the EGM field began with the emergence of a theory of entropy generation minimization in insulation systems subject to finite-size constraints. The development of this theory is reviewed in this chapter. The individual cryogenic engineering applications that stimulated the development of the theory are reviewed in Chapter 11.