The scientific study of morality requires measurement tools. But can we measure individual differences in something so seemingly subjective, elusive, and difficult to define? This paper will consider the prospects and challenges—both practical and ethical—of measuring how moral a person is. We outline the conceptual requirements for measuring general morality and argue that it would be difficult to operationalize morality in a way that satisfies these requirements. Even if we were able to surmount these conceptual challenges, self-report, informant report, behavioral, and biological measures each have methodological limitations that would substantially undermine their validity or feasibility. These challenges will make it more difficult to develop valid measures of general morality than other psychological traits. But, even if a general measure of morality is not feasible, it does not follow that moral psychological phenomena cannot or should not be measured at all. Instead, there is more promise in developing measures of specific operationalizations of morality (e.g., commonsense morality), specific manifestations of morality (e.g., specific virtues or behaviors), and other aspects of moral functioning that do not necessarily reflect moral goodness (e.g., moral self-perceptions). Still, it is important to be transparent and intellectually humble about what we can and cannot conclude based on various moral assessments—especially given the potential for misuse or misinterpretation of value-laden, contestable, and imperfect measures. Finally, we outline recommendations and future directions for psychological and philosophical inquiry into the development and use of morality measures.