While probabilistic models describe the dependence structure between observed variables, causal models go one step further: they predict, for example, how cognitive functions are affected by external interventions that perturb neuronal activity. In this review and perspective article, we introduce the concept of causality in the context of cognitive neuroscience and review existing methods for inferring causal relationships from data. Causal inference is an ambitious task that is particularly challenging in cognitive neuroscience. We discuss two difficulties in more detail: the scarcity of interventional data and the challenge of finding the right variables. We argue for distributional robustness as a guiding principle to tackle these problems. Robustness (or invariance) is a fundamental principle underlying causal methodology. A causal model of a target variable generalises across environments or subjects as long as these environments leave the causal mechanisms intact. Consequently, if a candidate model does not generalise, then either it does not consist of the target variable's causes or the underlying variables do not represent the correct granularity of the problem. In this sense, assessing generalisability may be useful when defining relevant variables and can be used to partially compensate for the lack of interventional data.