Criminal law consists of substantive and procedural parts. Substantive law is the set of rules defining conduct that violates the law. Procedural criminal law is the set of rules regulating the process of punishment. Substantive rules apply mostly to individual actors, and procedural rules apply to public enforcement agencies and adjudicators. Economic theory of criminal law consists of normative and positive parts. Normative economic theory, which began with writings by Beccaria and Bentham, aims to recommend an ideal criminal punishment scheme. Positive economic theory, which appeared later in writings by Holmes and Posner, aims to justify and to better understand the criminal law rules that exist. Since the purpose of criminal law is to deter socially undesirable conduct, economic theory, which emphasizes incentives, would appear to be an important perspective from which to examine criminal law. Positive economic theory, applied to substantive criminal law, seeks to explain and to justify criminal law doctrine in economic terms—that is, in terms that emphasize the incentive effects created by the law. The positive economic theory of criminal law literature can be divided into three phases: Classical deterrence theory, neoclassical deterrence, and modern synthesis. The modern synthesis provides a rationale for fundamental criminal law doctrines and also more puzzling portions of the law such as the doctrines of intent and necessity. Positive economic theory also provides a rationale for the allocation of enforcement responsibilities.