Since at least the middle of the past century, one overarching model of psychiatric classification, namely, that of the Diagnostic and Statistical Manual of Mental Disorders and International Classification of Diseases (DSM-ICD), has reigned supreme. This DSM-ICD approach embraces an Aristotelian view of mental disorders as largely discrete entities that are characterized by distinctive signs, symptoms, and natural histories. Over the past several years, however, a competing vision, namely, the Research Domain Criteria (RDoC) initiative launched by the National Institute of Mental Health, has emerged in response to accumulating anomalies within the DSM-ICD system. In contrast to DSM-ICD, RDoC embraces a Galilean view of psychopathology as the product of dysfunctions in neural circuitry. RDoC appears to be a valuable endeavor that holds out the long-term promise of an alternative system of mental illness classification. We delineate three sets of pressing challenges – conceptual, methodological, and logistical/pragmatic – that must be addressed for RDoC to realize its scientific potential, and conclude with a call for further research, including investigation of a rapprochement between Aristotelian and Galilean approaches to psychiatric classification.