It is known that hepatitis B virus (HBV) covalently closed circular DNA (cccDNA) persists in the nucleus of infected hepatocytes in the form of minichromosome and is difficult to target and eliminate. Studies on the mechanisms and strategies for persistent silencing or elimination of HBV cccDNA are the focus achieving for “functional cure” of chronic hepatitis B. This article introduces the current knowledge on the basic biological features of cccDNA, regulatory mechanisms of transcription and metabolism, and related host factors, with a focus on the potential pathways and strategies for cccDNA silencing or elimination.