This book focuses on a form of reasoning in science that I call “asymptotic reasoning.” At base, this type of reasoning involves methods that eliminate details and, in some sense, precision. Asymptotic reasoning has received systematic treatment in physics and applied mathematics, but virtually no attention has been paid to it by philosophers of science. I argue that once one understands the role played by asymptotic reasoning in explanatory arguments of scientists, our philosophical conceptions of explanation, reduction, and emergence require significant modification.