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We investigate the impacts of external forcings and internal climate variability (ICV) on global‐mean surface air temperature (GMST) variations (1850–2014) in observation and an ensemble of sixth Coupled Model Intercomparison Project (CMIP6) historical simulations. Using multiple regression models, we estimate that 83% of the observed GMST variance is explained by global‐scale anthropogenic forcing. Most CMIP6 models underestimate this anthropogenic contribution (median explained variance is 67%), but compare better with observation when the North Atlantic regional contribution is included in the anthropogenic forcing (median 77%). The ICV contributions to the GMST variance are ∼8% for observation and ∼7% for the models (median). The models' GMST responses to the external forcings and ICV vary widely, with the two responses being oppositely related. The North Atlantic predominantly drives the free GMST variability in observations, whereas the Pacific drives this in most CMIP6 models due to stronger than observed simulated GMST‐Pacific ICV relationships. Plain Language Summary: Global surface temperature has significantly warmed over the last one and a‐half centuries due to the combined effects of human produced greenhouse gases and aerosols and naturally occurring volcanic eruptions and solar output changes. These externally forced temperature changes are modulated by the climate system's internal variability. Most climate models simulate these different temperature changes, but with significant differences between the models' simulations. Here, we analyze data from observations and from simulations by 42 state‐of‐the‐art climate models to quantify the effects of external forcings and internal variability on surface temperature change. We find that most of the climate models underestimate the observed warming arising from global climate forcing but overestimate the multidecadal variations arising from North Atlantic aerosol forcing. The effect on temperature change from internal variability is much smaller than that from the combined external forcing, in both observations and climate models. Also, the models showing the largest temperature responses to external forcing show the smallest responses to internal variability, and vice‐versa. Understanding the reasons for these differences between climate simulations may help improve the confidence in climate change projections. Key Points: Most models underestimate (overestimate) the surface temperature response to global‐scale anthropogenic (North Atlantic regional) forcingThe models' diverse responses to external forcing have a strong negative relationship with the responses to internal variabilityThe North Atlantic (Pacific) internal variability dominates the unforced surface temperature variations in observations (most models) [ABSTRACT FROM AUTHOR]