Addictive diseases, including addiction to heroin, prescription opioids, or cocaine, pose massive personal and public health costs. Addictions are chronic relapsing diseases of the brain caused by drug-induced direct effects and persisting neuroadaptations at the epigenetic, mRNA, neuropeptide, neurotransmitter, or protein levels. These neuroadaptations, which can be specific to drug type, and their resultant behaviors are modified by various internal and external environmental factors, including stress responsivity, addict mindset, and social setting. Specific gene variants, including variants encoding pharmacological target proteins or genes mediating neuroadaptations, also modify vulnerability at particular stages of addiction. Greater understanding of these interacting factors through laboratory-based and translational studies have the potential to optimize early interventions for the therapy of chronic addictive diseases and to reduce the burden of relapse. Here, we review the molecular neurobiology and genetics of opiate addiction, including heroin and prescription opioids, and cocaine addiction.