Abstract: This article surveys the theory of the public enforcement of law--the use of public agents (inspectors, tax auditors, police, prosecutors) to detect and to sanction violators of legal rules. We first present the basic elements of the theory, focusing on the probability of imposition of sanctions, the magnitude and form of sanctions, and the rule of liability. We then examine a variety of extensions of the central theory, concerning accidental harms, costs of imposing fines, errors, general enforcement, marginal deterrence, the principal-agent relationship, settlements, self-reporting, repeat offenders, imperfect knowledge about the probability and magnitude of fines, and incapacitation.