Recurring episodes of excessive food intake in binge eating disorder can be understood through the lens of behavioral control systems: patients repeat maladaptive behaviors against their explicit intent. Self-report measures show enhanced impulsivity and compulsivity in binge eating (BE) but are agnostic as to the processes that might lead to impulsive and compulsive behavior in the moment. Task-based neurocognitive investigations can tap into those processes. In this systematic review, we synthesize neurocognitive research on behavioral impulsivity and compulsivity in BE in humans and animals, published between 2010-2020. Findings on impulsivity are heterogeneous. Findings on compulsivity are sparse but comparatively consistent, indicating an imbalance of goal-directed and habitual control as well as deficits in reversal learning. We urge researchers to address heterogeneity related to mood states and the temporal dynamics of symptoms, to systematically differentiate contributions of body weight and BE, and to ascertain the validity and reliability of tasks. Moreover, we propose to further scrutinize the compulsivity findings to unravel the computational mechanisms of a potential reinforcement learning deficit.