It is often presumed that the laws of nature have special significance for scientific reasoning. But the laws'distinctive roles have proven notoriously difficult : to pin downleading some philosophers to question if they perform such roles at all. This new study offers original accounts of the roles that natural laws play in connection with counterfactual conditionals, inductive projections, and scientific explanations, and of what the laws must be in order for them to be capable of playing these roles. Marc Lange shows that natural laws collectively possess a unique range of invariance under counterfactual perturbations, a range which is characterized for the first time without appealing to the concept of a law. Lange argues that the laws fail to supervene on the non-nomic facts, just as the rules governing chess fail to supervene on die moves made in a given actual game. He disputes both. regularity accounts and analyses of laws as relations among universals, contending that a possible world may include "offstage" violations of its laws. Lange also explains how a law of one scientific field can be an accident of another, and how a special science's autonomy makes its macro explanations irreducible to the micro explanations supplied. by fundamental physics. Particular attention is given to grades of physical necessity, laws concerning particular biological species, natural kinds, ceteris-paribus clauses, the paradoxes of confirmation, physically necessary coincidences, and laws about laws. Major figures in the philosophy of science receive special discussion, including Lewis, Goodman, van Fraassen, Armstrong, Dretske, Earman, Mill, Fodor, Hempel, Giere, Putnam, Dennett, and Mackie. Lange's innovative account of the roles that natural laws play in scientific reasoning is must reading for philosophers of science and will interest metaphysicians, epistemologists, and philosophers of social science, as well as biologists, physicists, and historians of science.