Chronic hepatitis B virus (HBV) infection continues to be a major health burden worldwide; it can cause various degrees of liver damage and is strongly associated with the development of liver cirrhosis and hepatocellular carcinoma. The molecular mechanisms determining HBV persistence are not fully understood, but these appear to be multifactorial and the unique replication strategy employed by HBV enables its maintenance in infected hepatocytes. Both the stability of the HBV genome, which forms a stable minichromosome, the covalently closed circular DNA (cccDNA) in the hepatocyte nucleus, and the inability of the immune system to resolve chronic HBV infection are believed to be key mechanisms of HBV chronicity. Since a true cure of HBV requires clearance of intranuclear cccDNA from infected hepatocytes, understanding the mechanisms involved in cccDNA biogenesis, regulation and stability is mandatory to achieve HBV eradication. This review will summarize the state of knowledge on these mechanisms including the impact of current treatments on the cccDNA stability and activity. We will focus on events challenging cccDNA persistence in dividing hepatocytes.