 Section 1  begins with a working definition of counterfactual conditionals  (§1.1),  and then surveys how counterfactuals feature in theories of agency, mental representation, and rationality  (§1.2),  and how they are used in metaphysical analysis and scientific explanation  (§1.3).  Section 1.4 then details several ways in which the logic and truth-conditions of counterfactuals are puzzling. This sets the stage for the sections  2  and  3,  which survey semantic analyses of counterfactuals that attempt to explain this puzzling behavior.