We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). 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. By selecting the combination of climatic variables and the regions of interest, it is possible to highlight specific model deficiencies. The WD enables a comprehensive evaluation of the skill of a climate model. We apply this approach to a selected number of physical fields, ranking the models in terms of their performance in simulating them and pinpointing their weaknesses in the simulation of some of the selected physical fields in specific areas of the Earth.