Today it is well acknowledged that both nature and nurture play important roles in the genesis of psychopathologies, including drug addiction. Increasing evidence suggests that genetic factors contribute for at least 40–60% of the variation in liability to drug dependence. Human genetic studies suggest that multiple genes of small effect, rather than single genes, contribute to the genesis of behavioral psychopathologies. Therefore, the use of inbred rat strains might provide a valuable tool to identify differences, linked to genotype, important in liability to addiction and related disorders. In this regard, Lewis and Fischer 344 inbred rats have been proposed as a model of genetic vulnerability to drug addiction, given their innate differences in sensitivity to the reinforcing and rewarding effects of drugs of abuse, as well their different responsiveness to stressful stimuli. This review will provide evidence in support of this model for the study of the genetic influence on addiction vulnerability, with particular emphasis on differences in mesolimbic dopamine (DA) transmission, rewarding and emotional function. It will be highlighted that Lewis and Fischer 344 rats differ not only in several indices of DA transmission and adaptive changes following repeated drug exposure, but also in hypothalamic-pituitary-adrenal (HPA) axis responsiveness, influencing not only the ability of the individual to cope with stressful events, but also interfering with rewarding and motivational processes, given the influence of corticosteroids on dopamine neuron functionality. Further differences between the two strains, as impulsivity or anxiousness, might contribute to their different proneness to addiction, and likely these features might be linked to their different DA neurotransmission plasticity. Although differences in other neurotransmitter systems might deserve further investigation, results from the reviewed studies might open new vistas in understanding aberrant deviations in reward and motivational functions.