The development of animal models of drug reward and addiction is an essential factor for progress in understanding the biological basis of this disorder and for the identification of new therapeutic targets. Depending on the component of reward to be studied, one type of animal model or another may be used. There are models of reinforcement based on the primary hedonic effect produced by the consumption of the addictive substance, such as the self-administration (SA) and intracranial self-stimulation (ICSS) paradigms, and there are models based on the component of reward related to associative learning and cognitive ability to make predictions about obtaining reward in the future, such as the conditioned place preference (CPP) paradigm. In recent years these models have incorporated methodological modifications to study extinction, reinstatement and reconsolidation processes, or to model specific aspects of addictive behavior such as motivation to consume drugs, compulsive consumption or drug seeking under punishment situations. There are also models that link different reinforcement components or model voluntary motivation to consume (two-bottle choice, or drinking in the dark tests). In short, innovations in these models allow progress in scientific knowledge regarding the different aspects that lead individuals to consume a drug and develop compulsive consumption, providing a target for future treatments of addiction.