Characteristics and trends of surface ocean dimethylsulfide (DMS) concentrations and fluxes into the atmosphere of four Earth system models (ESMs: CNRM-ESM2-1, MIROC-ES2L, NorESM2-LM, and UKESM1-0-LL) are analysed over the recent past (1980–2009) and into the future, using Coupled Model Intercomparison Project 6 (CMIP6) simulations. The DMS concentrations in historical simulations systematically underestimate the most widely used observed climatology but compare more favourably against two recent observation-based datasets. The models better reproduce observations in mid to high latitudes, as well as in polar and westerlies marine biomes. The resulting multi-model estimate of contemporary global ocean DMS emissions is 16–24 Tg S yr−1, which is narrower than the observational-derived range of 16 to 28 Tg S yr−1. The four models disagree on the sign of the trend of the global DMS flux from 1980 onwards, with two models showing an increase and two models a decrease. At the global scale, these trends are dominated by changes in surface DMS concentrations in all models, irrespective of the air–sea flux parameterisation used. In turn, three models consistently show that changes in DMS concentrations are correlated with changes in marine productivity; however, marine productivity is poorly constrained in the current generation of ESMs, thus limiting the predictive ability of this relationship. In contrast, a consensus is found among all models over polar latitudes where an increasing trend is predominantly driven by the retreating sea-ice extent. However, the magnitude of this trend between models differs by a factor of 3, from 2.9 to 9.2 Gg S decade−1 over the period 1980–2014, which is at the low end of a recent satellite-derived analysis. Similar increasing trends are found in climate projections over the 21st century.