The feeding process is required for basic life, influenced by environment cues and tightly regulated according to demands of the internal milieu by regulatory brain circuits. Although eating behaviour cannot be considered "addictive" under normal circumstances, people can become "addicted" to this behaviour, similarly to how some people are addicted to drugs. The symptoms, cravings and causes of "eating addiction" are remarkably similar to those experienced by drug addicts, and both drug-seeking behaviour as eating addiction share the same neural pathways. However, while the drug addiction process has been highly characterised, eating addiction is a nascent field. In fact, there is still a great controversy over the concept of "food addiction". This review aims to summarize the most relevant animal models of "eating addictive behaviour", emphasising binge eating disorder, that could help us to understand the neurobiological mechanisms hidden under this behaviour, and to improve the psychotherapy and pharmacological treatment in patients suffering from these pathologies.