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The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers.