Global prophylactic vaccination programmes have helped to curb new hepatitis B virus (HBV) infections. However, it is estimated that nearly 300 million people are chronically infected and have a high risk of developing hepatocellular carcinoma. As such, HBV remains a serious health priority and the development of novel curative therapeutics is urgently needed. Chronic HBV infection has been attributed to the persistence of the covalently closed circular DNA (cccDNA) which establishes itself as a minichromosome in the nucleus of hepatocytes. As the viral transcription intermediate, the cccDNA is responsible for producing new virions and perpetuating infection. HBV is dependent on various host factors for cccDNA formation and the minichromosome is amenable to epigenetic modifications. Two HBV proteins, X (HBx) and core (HBc) promote viral replication by modulating the cccDNA epigenome and regulating host cell responses. This includes viral and host gene expression, chromatin remodeling, DNA methylation, the antiviral immune response, apoptosis, and ubiquitination. Elimination of the cccDNA minichromosome would result in a sterilizing cure; however, this may be difficult to achieve. Epigenetic therapies could permanently silence the cccDNA minichromosome and promote a functional cure. This review explores the cccDNA epigenome, how host and viral factors influence transcription, and the recent epigenetic therapies and epigenome engineering approaches that have been described.