We propose a methodology for evaluating the performance of climate models based on the use of the Wasserstein distance. This distance provides a rigorous way to measure quantitatively the difference between two probability distributions. The proposed approach is flexible and can be applied in any number of dimensions; it allows one to rank climate models taking into account all the moments of the distributions. Furthermore, by selecting the combination of climatic variables and the regions of interest, it is possible to highlight the deficiencies of each of the models under study. The Wasserstein distance thus enables a comprehensive evaluation of climate model skill. We apply this approach to a selected number of physical fields, ranking the models in terms of their performance in simulating them, as well as pinpointing their weaknesses in the simulation of some of the selected physical fields in specific areas of the Earth.