Based on data of bryophyte invasions into 82 regions on five continents of both hemispheres, we aim here at a first comprehensive overview of the impacts that bryophytes may have on biodiversity and socio-economy. Of the 139 bryophytes species which are alien in the study regions seven cause negative impacts on biodiversity in 26 regions, whereas three species cause negative impacts on socio-economic sectors in five regions. The vast majority of impacts stem from anecdotal observations, whereas only 14 field or experimental studies (mostly on Campylopus introflexus in Europe) have quantitatively assessed the impacts of an alien bryophyte. The main documented type of impact on biodiversity is competition (8 alien bryophytes), with native cryptogams being most affected. In particular, C. introflexus (9 regions) and Pseudoscleropodium purum (7 regions) affect resident species composition. The few socio-economic impacts are caused by alien bryophytes which form dense mats in lawns and are then considered a nuisance. Most negative impacts on biodiversity have been recorded in natural grasslands, forests, and wetlands. Impacts of alien bryophytes on biodiversity and socio-economy are a recent phenomenon, with >85 % of impacts on biodiversity, and 80 % of impacts on socio-economy recorded since 1990. On average, 40 years (impacts on biodiversity) and 25 years (impacts on socio-economy) elapsed between the year a bryophyte species has been first recorded as alien in a region and the year impacts have been recorded first. Taking into account the substantial time lag between first record and first recorded impact in a region, it seems to be likely that the currently moderate impacts of alien bryophytes will continue to increase. As quantitative studies on impacts of alien bryophytes are rare and restricted to few environments and biogeographic regions, there is a need for addressing potential impacts of alien bryophytes in yet understudied settings.