Climate classifications based on temperature and precipitation measurements are increasingly being used for environmental and climate change studies. Using three classification methods (Klippen, Extended Klippen, and Holdridge) and one observational dataset for present climate (CRU, Climate Research Unit), we show that GCMs have bridged the gap that led to the emergence of RCMs thirty years ago, as GCMs can now provide global climate classifications whose accuracy and precision are comparable to those of regional outputs of the RCMs. Projections of high-resolution GCMs for future climates under the assumptions of three Representative Concentration Pathways (RCP26, RCP45 and RCP85) can therefore be used as a primary source for climate change and global warming studies at high resolution. This paper provides comprehensive, model-derived climate classifications for the entire planet, using RCMs and two GCMs for present and future climate-change scenarios, and discusses how well the models actually represent the climates of the world when compared with reference, ground validation data. It turns out that both GCMs and RCMs appear still limited to provide practical estimates of the world climates even for present climate conditions. The modeling of precipitation remains the Achilles' heel of models and thus of multidimensional indices, which are very sensitive to this variable. The conclusion is that model outputs at regional scale need to be taken with extreme caution without venturing into informing policies presenting potentially large societal impacts. Nonetheless, the role of models as privileged tools to advance our scientific knowledge of the Earth's system remains undisputed.