The co-occurrence of drug addiction in adults with attention deficit hyperactivity disorder (ADHD) is very common, but its etiology remains largely unknown. Therefore, animal models to study this kind of psychiatric comorbidity are needed. The Spontaneously Hypertensive Rat (SHR) strain shows neurochemical and behavioral characteristics which make it a suitable model of ADHD. Compared with their normotensive controls (Wistar-Kyoto) and with some other rat strains, SHR rats drink more ethanol and are more sensitive to its anxiolytic/stimulant effects. They also show increased sensitivity to psychostimulants, opioids and cannabinoids. Furthermore, chronic treatment with methylphenidate, the first-choice drug to treat ADHD, during adolescence, changes the ethanol intake and the behavioral effects of cocaine in adult SHR rats. Regarding sex differences, females are more sensitive to psychostimulants and drink more ethanol than males, an important condition because in adulthood, more females suffer from ADHD than males. Taken together, the reviewed findings indicate that the SHR strain is a promising tool for studies on drug addiction and, possibly, its relationship with ADHD.