 Because this is a particularly long and dense section of the article, we begin with an outline of it.  Section 5.1  states the laws of black holes in classical general relativity, and expounds the formal analogy they stand in with the laws of ordinary thermodynamics.  Section 5.2  briefly describes how taking account of quantum effects in the neighborhood of a black hole leads to the prediction of Hawking radiation and the subsequent conclusion that the analogy with the laws of ordinary thermodynamics is more than just formal, but represents a true and intimate physical connection.  Section 5.3  discusses the puzzles that arise when trying to understand the attribution of a physical entropy to a black hole.  Section 5.4  consists of several subsections, each examining a different puzzling aspect of the so-called Generalized Second Law: the hypothesis that the total entropy of the universe, that of ordinary matter plus that of black holes, never decreases. We conclude in  Section 5.5  with a brief account of attempts to extend the attribution of a physical entropy to gravitational systems more general than just black holes. 