A widely accessible authoritative list of known plant species is a fundamental requirement for local, regional, and global biodiversity conservation efforts. The longstanding index series of published names of liverworts and hornworts continues with 2019 and 2020. The list herein includes one higher taxon name, six generic names, 13 infrageneric names, 124 specific names, 27 infraspecific names, one infrageneric autonym and nine infraspecific autonyms for 2019 and 2020. The list includes 13 names of fossils as well as 13 invalid names. Four older names omitted in the earlier indices are included.