Addiction is a mental disorder described as a disease in which, after a period of recreational use, an individual develops compulsive use that does not stop even in the face of major negative consequences. Although the development of addiction involves many genetic and environmental factors, its mechanism is not yet fully understood. This paper provides an overview of the latest research and findings on structural, biochemical, genetic and epigenetic changes of the brain during the development of addiction. Structural changes involve changes in number and function of neurons or synapses, as well as changes in specific brain region activity, while biochemical ones include changes in metabolism and function of neurotransmitters and hormones. Genetic changes refer to reduced expression or polymorphisms of genes that regulate the metabolism and activity of neurotransmitters involved in the development of addiction, and epigenetic changes to long-term changes in gene expression due to drug consumption or stress. Various approaches to therapy and treatment of the addiction are known, but none are fully effective to date. The challenge of relapse continues to greatly hinder the recovery of an addict. Therefore, further research is needed, which will provide a better understanding of the underlying mechanisms and connection of addiction with cellular and molecular pathways in the brain and its impact on the neuroanatomical structure of the brain, in order to develop more effective treatment strategies for this widespread and complex disorder.