Recent experiments have shown that when individuals with a substance use disorder are confronted with drug-related cues, they exhibit an automatically activated tendency to approach these cues (i.e., drug approach bias). The strength of the drug approach bias has been associated with clinically relevant measures, such as increased drug craving and relapse, and activations in brain reward areas. Retraining the approach bias by means of cognitive bias modification has been demonstrated to decrease relapse rates in patients with an alcohol use disorder and to reduce alcohol cue-evoked limbic activity. Here, we review empirical and theoretical literature on the drug approach bias and explore two distinct models of how the drug approach bias may be embodied. First, we consider the "biological meaning" hypothesis, which grounds the automatic approach bias in the natural meaning of the body. Second, we consider the "sensorimotor hypothesis," which appeals to the specific sensorimotor loops involved in the instantiation of addictive behaviors as the basis of the automatic approach bias. In order to differentiate between the adequacies of these competing explanations, we present specific, predictions that each model should make.