Bat hepadnaviruses and the origins of primate hepatitis B viruses

•Bat hepadnaviruses are genetically more diverse than other extant hepadnaviruses.•Ancestral hepadnaviruses are present in diverse chiropteran clades.•Hepadnavirus host switches likely occurred within primates and bats.•Primates may have acquired hepadnaviruses from bats.•Major parts of orthohepadnavirus evolution took place in the New World.