It has been over 50 years since the discovery of hepatitis B virus (HBV), yet 240 million people worldwide live with chronic HBV, resulting in up to 800 000 deaths per year. A cure is yet to be achieved, due largely to a viral nuclear reservoir of transcriptionally active covalently closed circular DNA (cccDNA). While current antiviral therapies are effective at reducing viral replication, they have no impact on the existing cccDNA reservoir. Identifying mechanisms to either eliminate (complete cure) or inactivate (functional cure) HBV cccDNA are a major focus of HBV research worldwide. This review discusses recent advances in efforts to eliminate and/or regulate cccDNA, as well as future directions that may be considered in efforts to cure chronic HBV.