 That black holes and other purely gravitational and geometrical systems possess an entropy naturally leads to the idea that the Second Law of thermodynamics ought to be modified in order to accommodate that fact. It is an almost completely unexplored issue how this Generalized Second Law itself may require modifications to the traditional questions about the Second Law, and possibly lead to new insights about them. Thus the postulation of the Generalized Second Law and its broad acceptance by the physics community raises many interesting puzzles and questions. 