Climate models often exhibit spurious long-term changes independent of either internal variability or changes to external forcing. Such changes, referred to as model drift, may distort the estimate of forced change in transient climate simulations. The importance of drift is examined in comparison to historical trends over recent decades in the Coupled Model Intercomparison Project (CMIP). Comparison based on a selection of metrics suggests a significant overall reduction in the magnitude of drift from phase 3 of CMIP (CMIP3) to phase 5 of CMIP (CMIP5). The direction of both ocean and atmospheric drift is systematically biased in some models introducing statistically significant drift in globally averaged metrics. Nevertheless, for most models globally averaged drift remains weak compared to the associated forced trends and is often smaller than the difference between trends derived from different ensemble members or the error introduced by the aliasing of natural variability. An exception to this is metrics that include the deep ocean (e.g., steric sea level) where drift can dominate in forced simulations. In such circumstances drift must be corrected for using information from concurrent control experiments. Many CMIP5 models now include ocean biogeochemistry. Like physical models, biogeochemical models generally undergo long spinup integrations to minimize drift. Nevertheless, based on a limited subset of models, it is found that drift is an important consideration and must be accounted for. For properties or regions where drift is important, the drift correction method must be carefully considered. The use of a drift estimate based on the full control time series is recommended to minimize the contamination of the drift estimate by internal variability.