Although Buying Disorder (BD) is not a formal diagnosis in commonly used diagnostic systems, this condition can cause significant impairments. Additionally, there is an ongoing discussion about the most appropriate conceptualization and classification of BD. Most often, BD is considered either an obsessive–compulsive and related disorder (OCRD) or an addictive behavior (i.e., substance use disorders or behavioral addictions), and was previously recognized as an impulse control disorder. The present narrative review examines the cognitive processes of impulsivity (i.e., impulsive action, impulsive choice, decision making, and personality), compulsivity, and reward processing (i.e., cue reactivity and craving), in BD, obsessive–compulsive disorder (OCD), and addictive behaviors. Most evidence supports BD having overlapping features with behavioral addictions more so than with OCD due to similar impairments in decision-making and inhibition, as well as similar motivations behind BD. Further, BD demonstrates cue-reactivity and craving similar to behavioral addictions. There were also similar elevations on personality inventories between BD and addictive behaviors, which were less relevant in OCD. Although studies in these specific cognitive domains suggest similarities between BD and behavioral addiction, more studies are needed to further elucidate BD processes, which would in turn assist with the classification of BD. Further, despite similarities across conditions, directly comparing BD to these conditions on the aforementioned processes is needed. In future, study designs should directly compare BD to disorders within each classification to elucidate shared and distinct functions of these processes.