In climate science, climate models are one of the main tools for understanding phenomena. Here, we develop a framework to assess the fitness of a climate model for providing understanding. The framework is based on three dimensions: representational accuracy, representational depth, and graspability. We show that this framework does justice to the intuition that classical process-based climate models give understanding of phenomena. While simple climate models are characterized by a larger graspability, state-of-the-art models have a higher representational accuracy and representational (...) depth. We then compare the fitness-for-providing understanding of process-based to data-driven models that are built with machine learning. We show that at first glance, data-driven models seem either unnecessary or inadequate for understanding. However, a case study from atmospheric research demonstrates that this is a false dilemma. Data-driven models can be useful tools for understanding , specifically for phenomena for which scientists can argue from the coherence of the models with background knowledge to their representational accuracy and for which the model complexity can be reduced such that they are graspable to a satisfactory extent. When citing this paper, please use the full journal title Studies in History and Philosophy of Science. (shrink)