The heightened incidence of opioid use during pregnancy has resulted in unprecedented rates of neonates prenatally exposed to opioids. Prenatal opioid exposure (POE) results in significantly adverse medical, developmental, and behavioral outcomes in offspring. Of growing interest is whether POE contributes to future vulnerability to substance use disorders. The effects of POE on brain development is difficult to assess in humans, as the timing, dose, and route of drug exposure together with complex genetic and environmental factors affect susceptibility to addiction. Preclinical models of POE have allowed us to avoid methodological difficulties and confounding factors of POE in humans. Here, we review the effects of maternal opioid exposure on the developing brain with an emphasis on the neurobiological basis of drug addiction and on preclinical models of POE and their limitations. These studies have indicated that POE increases self-administration of drugs, reward-driven behaviors in the conditioned place paradigm, and locomotor sensitization. While addiction is multifaceted and vulnerability to drug addiction is still inconclusive in human studies of prenatally exposed infants, animal studies do provide a noteworthy corroboration of negative behavioral outcomes.