We analyse and document the historical simulations performed by two versions of the Australian Community Climate and Earth System Simulator (ACCESS-CM2 and ACCESS-ESM1.5) for the Coupled Model Intercomparison Project Phase 6 (CMIP6). Three ensemble members from each model are used to compare the simulated seasonal-mean climate, climate variability and climate change with observations over the historical period. Where appropriate, we also compare the ACCESS model results with the results from 36 other CMIP6 models. We find that the simulations of the winter and summer mean climates (over the global domain) by the two ACCESS models are similar to or better than most of the other CMIP6 models for surface temperature, precipitation and surface specific humidity. For sea-level pressure, both ACCESS models perform worse than most other models. The spatial structures of the prominent climate variability modes (ENSO, IOD, IPO and AMO) also compare favourably with the corresponding observed structures. However, the results for the simulation of the models’ temporal variability are mixed. In particular, whereas ACCESS-ESM1.5 simulates ENSO events with ~3-year periods (that are closer to the observed periods of 3–7 years), the ACCESS-CM2 simulates ENSO events having quasi-biennial periods. However, ACCESS-CM2 has a much smaller bias (−0.1 W m−2) in present-day top-of-the-atmosphere energy balance than ACCESS-ESM1.5 (−0.6 W m−2). The ACCESS models simulate the anthropogenic climate change signal in historical global-mean surface temperature reasonably well, although the simulated signal variances are ~10% weaker than the observed signal variance (a common bias in most CMIP6 models). Both models also well simulate the major features of observed surface temperature changes, as isolated using a multiple regression model. Despite some identified biases, the two ACCESS models provide high-quality climate simulations that may be used in further analyses of climate variability and change.