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Climate classifications are useful to synthesize the physical state of the climate with a proxy that can be directly related to biota. However, they present a potential drawback, namely a strong sensitivity because of the use of hard thresholds (step functions). Thus, minor discrepancies in the base data produce large differences in the type of climate. However, such an a priori limitation is also a strength because such sensitivity can be used to better gauge model performance. Although previous attempts of classifying climates of the world using global climate model outputs were encouraging, the applicability of their classifications to impact studies has been limited by past model issues. Notwithstanding the persistence of certain imperfections and limitations in current models, the high‐quality physical simulations from phase six of the Coupled Intercomparison Project (CMIP6) has opened new possibilities in the field, thanks to their improved representation of atmospheric and oceanic physics. The purpose of this paper is twofold: to show that climate classifications from CMIP6 are sufficiently robust for use in impact studies, and to use those classifications for identifying error sources and potential issues that deserve further attention in models. Thus, 52 CMIP6 climate models were evaluated by using three climate classifications schemes, classical Köppen, extended‐Köppen, and modified Thornthwaite. We first assessed model ability to reproduce present climate types by comparing their outputs with observational data. Models performed best for the Köppen and extended‐Köppen classification methods (Cohen's kappa κ = 0.7), and had moderate scores for the Thornthwaite climate classification (κ = 0.4). By tracing back the observed biases, we were able to pinpoint the misrepresentation of dry climates as a major source of error. Another finding was that most models still had some difficulties in representing the seasonal variability of precipitation over several monsoonal regions, thereby yielding the wrong climate type there. Models were also evaluated for future climate. Substantial changes in climate types are projected in the SSP5‐8.5 scenario. These changes include a shrinkage of polar/frigid climates (22%) and an increase of dry climates (7%). [ABSTRACT FROM AUTHOR]