Some bryophyte taxa in Australia exhibit weedy characteristics and have been considered variously in literature for their adventive distributions following European occupation. A total of 29 taxa are considered here. These include 13 taxa that are regarded as exotic throughout Australia. Two taxa have a reported cosmopolitan distribution, while 14 have cryptogenic or dual origin status but are not suspected to be native to all or part of their current range within Australia. The basis for treating some taxa as introduced is subjectively based on their pattern of distribution outside Australia and their association with anthropogenic habitats within Australia. Factors for consideration regarding the detection and reporting of adventive bryophytes are discussed. Their impact on Australian ecosystems is largely speculative. In the absence of quantitative research there is, unsurprisingly, little attention given to the need or methods for their management. (The Victorian Naturalist 137 (6), 2020, 179-194) Keywords: bryophytes, introduced species, weeds, Pseudoscleropodium purum