The downward trend in Arctic sea ice extent is one of the most dramatic signals of climate change during recent decades. Comprehensive climate models have struggled to reproduce this trend, typically simulating a slower rate of sea ice retreat than has been observed. However, this bias has been widely noted to have decreased in models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5) compared with the previous generation of models (CMIP3). The ensemble-mean Arctic sea ice trend in CMIP5 is still slower than observed, yet there is a small subset of model simulations that have sea ice trends similar to the observations. Based on this, a number of recent studies have suggested that the models are consistent with the observations when simulated internal climate variability is taken into account. We visit each of these results, drawing on previous work that found a close relationship in climate models between global-mean surface temperature and sea ice extent, and find that this leads to different conclusions. We examine sea ice changes in simulations from CMIP3, CMIP5, and the Community Earth System Model Large Ensemble (CESM-LE). First, we find that all of the simulations with 1979-2013 Arctic sea ice retreat as fast as observed have considerably more global warming than observations during this time period. Using two separate methods to estimate the sea ice retreat that would occur under the observed level of global warming in each simulation in both ensembles, we find that simulated Arctic sea ice retreat as fast as observed would occur less than 1% of the time. This implies that the models are not consistent with the observations. In the Antarctic, we find that simulated sea ice expansion as fast as observed typically corresponds with too little global warming, although these results are more equivocal. We show that because of this, the simulations do not capture the observed asymmetry between Arctic and Antarctic sea ice trends. Second, we find that simulated historical sea ice trends are influenced by volcanic forcing, which was included in all of the CMIP5 models but in only about half of the CMIP3 models. The volcanic forcing causes temporary simulated cooling in the 1980s and 1990s, which contributes to raising the simulated 1979–2013 global-mean surface temperature trends to values substantially larger than observed. It is shown that this warming bias is accompanied by an enhanced rate of Arctic sea ice retreat and hence a simulated sea ice trend that is closer to the observed value. The results imply that much of the difference in Arctic sea ice trends between CMIP3 and CMIP5 occurred because of the inclusion of volcanic forcing, rather than improved sea ice physics or model resolution.