Research has focused on understanding how overeating can affect brain reward mechanisms and subsequent behaviors, both preclinically and in clinical research settings. This work is partly driven by the need to uncover the etiology and possible treatments for the ongoing obesity epidemic. However, overeating, or non-homeostatic feeding behavior, can occur independent of obesity. Isolating the variable of overeating from the consequence of increased body weight is of great utility, as it is well known that increased body weight or obesity can impart its own deleterious effects on physiology, neural processes, and behavior. In this review, we present data from three selected animal models of normal-weight non-homeostatic feeding behavior that have been significantly influenced by Bart Hoebel’s 40+-yr career studying motivation, feeding, reinforcement, and the neural mechanisms that participate in the regulation of these processes. First, a model of sugar bingeing is described (Avena/Hoebel), in which animals with repeated, intermittent access to a sugar solution develop behaviors and brain changes that are similar to the effects of some drugs of abuse, serving as the first animal model of food addiction. Second, another model is described (Boggiano) in which a history of dieting and stress can perpetuate further binge eating of palatable and non-palatable food. In addition, a model (Boggiano) is described that allows animals to be classified as having a binge-prone vs. binge-resistant phenotype. Lastly, a limited access model is described (Corwin) in which non-food deprived rats with sporadic limited access to a high-fat food develop binge-type behaviors. These models are considered within the context of their effects on brain reward systems, including dopamine, the opioids, cholinergic systems, serotonin, and GABA. Collectively, the data derived from the use of these models clearly show that behavioral and neuronal consequences of bingeing on a palatable food, even when at a normal body weight, are different from those that result from simply consuming the palatable food in a non-binge manner. These findings may be important in understanding how overeating can influence behavior and brain chemistry.