What is the difference of a prediction that is made with a causal model and a\nnon-causal model? Suppose we intervene on the predictor variables or change the\nwhole environment. The predictions from a causal model will in general work as\nwell under interventions as for observational data. In contrast, predictions\nfrom a non-causal model can potentially be very wrong if we actively intervene\non variables. Here, we propose to exploit this invariance of a prediction under\na causal model for causal inference: given different experimental settings (for\nexample various interventions) we collect all models that do show invariance in\ntheir predictive accuracy across settings and interventions. The causal model\nwill be a member of this set of models with high probability. This approach\nyields valid confidence intervals for the causal relationships in quite general\nscenarios. We examine the example of structural equation models in more detail\nand provide sufficient assumptions under which the set of causal predictors\nbecomes identifiable. We further investigate robustness properties of our\napproach under model misspecification and discuss possible extensions. The\nempirical properties are studied for various data sets, including large-scale\ngene perturbation experiments.\n