This chapter clarifies the theoretical arguments through discussion of issues and questions that may arise in conceptualizing, testing, and evaluating not only comprehensive deterrence theory (CDT) but also, more generally, that can arise in deterrence research. For example, it discusses the nature of punishment. Deterrence scholarship understandably has examined the idea that punishments may deter. What has not been systematically theorized or empirically studied is punishment itself. Historical accounts exist, of course. And numerous scholars certainly have detailed many aspects of certain types of punishment, such as the death penalty. However, deterrence scholarship lacks a coherent foundation for predicting the effects of a wide variety of legal punishments, or how to distinguish when one type of punishment meaningfully differs from another. Similarly, there is a great deal of confusion about legal vs. extralegal punishment as well as specific vs. general deterrence. The chapter examines these and other issues with an eye towards clarifying CDT and charting directions for improving deterrence scholarship.