Abstract: This chapter reviews the key findings of the optimal deterrence theory and discusses the remaining challenges. Some of these challenges reflect current modeling choices and limitations. These include the treatment of the offender’s gains in the social welfare function; the design of the damages multiplier in a realistic, multi-period framework; the effects of different types of uncertainty on behavior; and the study of optional, imperfectly enforced, threshold-based regimes – that is, regimes that reflect the most common real-world regulatory setting. Other challenges arise because several key regulatory features and enforcement outcomes are inconsistent with the deterrence theory’s predictions and prescriptions. These inconsistencies include the “abnormally” high levels of compliance, the pervasiveness of gain-based (rather than harm-based) sanctions, the widespread use of offense history in sanctions design, the variation of sanctions based on legal aggressiveness, and the significance of the offender’s mental state in the determinations of both liability and sanctions. The chapter discusses how the recent optimal deterrence scholarship has addressed – but has not fully resolved – all these challenges.