Hepatitis B virus (HBV) remains a significant cause of mortality and morbidity worldwide, since chronic HBV infection is associated with elevated risk of cirrhosis and hepatocellular carcinoma. Current licensed therapies against HBV efficiently suppress viral replication; however, they do not have significant effects on the intrahepatic covalently closed circular DNA (cccDNA) of the viral minichromosome responsible for viral persistence. Thus, life-long treatment is required to avoid viral rebound. There is a significant need for novel therapies that can reduce, silence or eradicate cccDNA, thus preventing HBV reemergence after treatment withdrawal. In this review, we discuss the latest developments and applications of gene editing and related approaches for directly targeting HBV DNA and, more specifically, cccDNA in infected hepatocytes.