Purpose: The purpose of this paper is to discuss the neuroscience and neurobiology of alcohol and drug addiction. The study of neuroscience and neurobiology of alcohol and drug addiction will help to understand the relationship between addiction and brain functioning. Methodology: The study utilized a systematic review of literature to study alcohol and drug addiction by identifying parts of the human brain responsible for addiction, stages of addiction, elements of addiction, and effects of different drugs on the brain. The main theories of addiction guiding the research were the Incentive-Sensitization theory and the Disease Theory. Findings: The outcome from the paper showed addiction is a chronic illness that contributes to significant impairments in social function, health, and in lack of control over drug use. The three stages of addiction are intoxication/ binge, withdrawal, and anticipation. Also, it was found out basal ganglia, extended amygdala, and the prefrontal cortex are the main parts of the brain responsible for drug addiction. Unique Contribution to Theory, Practice and Policy: The outcome from the paper has contributed towards advancing the knowledge of drug addiction by establishing evidence-based approaches for identifying the neurobiology and neuroscience of drug addiction. Findings can be utilized in developing policies and frameworks that guide the use of drugs, especially prescription drugs like opioids. Moreover, findings help in advancing the practice in medicine by recommending new pharmacological and non-pharmacological treatments to prevent and control addiction.