Cognitive impairments in substance use disorders have been extensively researched, especially since the advent of cognitive and computational neuroscience and neuroimaging methods in the last 20 years. Conceptually, altered cognitive function can be viewed as a hallmark feature of substance use disorders, with documented alterations in the well-known “executive” domains of attention, inhibition/regulation, working memory, and decision-making. Poor cognitive (sometimes referred to as “top-down”) regulation of downstream motivational processes—whether appetitive (reward, incentive salience) or aversive (stress, negative affect)—is recognized as a fundamental impairment in addiction and a potentially important target for intervention. As addressed in this special issue, cognitive impairment is a transdiagnostic domain; thus, advances in the characterization and treatment of cognitive dysfunction in substance use disorders could have benefit across multiple psychiatric disorders. Toward this general goal, we summarize current findings in the abovementioned cognitive domains of substance use disorders, while suggesting a potentially useful expansion to include processes that both precede(precognition) and supersede(social cognition) what is usually thought of as strictly cognition. These additional two areas have received relatively less attention but phenomenologically and otherwise are important features of substance use disorders. The review concludes with suggestions for research and potential therapeutic targeting of both the familiar and this more comprehensive version of cognitive domains related to substance use disorders.