Addictions are highly heritable disorders, with heritability estimates ranging from 39% to 72%. Multiple studies suggest a link between paternal drug abuse and addiction in their children. However, patterns of inheritance cannot be explained purely by Mendelian genetic mechanisms. Exposure to drugs of abuse results in epigenetic changes that may be passed on through the germline. This mechanism of epigenetic transgenerational inheritance may provide a link between paternal drug exposure and addiction susceptibility in the offspring. Recent studies have begun to investigate the effect of paternal drug exposure on behavioral and neurobiological phenotypes in offspring of drug-exposed fathers in rodent models. This review aims to discuss behavioral and neural effects of paternal exposure to alcohol, cocaine, opioids, and nicotine. Although a special focus will be on addiction-relevant behaviors, additional behavioral effects including cognition, anxiety, and depressive-like behaviors will be discussed.