Causal discovery algorithms seek to solve the following problem: from the observed correlations among a set of variables, infer the causal relations that hold among these. It is a problem of fundamental importance in all scientific fields wherein statistical data is prominent, including physics. The task can be intractable even in seemingly simple scenarios: for two correlated classical variables, it is impossible to determine by observation alone whether the correlation arose from a causal influence of one on the other or a common cause influencing both. In the quantum analogue of this problem, however, one *can* distinguish a cause-effect relation from a common-cause relation based on features of the observed correlations. This constitutes a quantum advantage for causal discovery. I discuss the results of a quantum-optical experiment wherein we vary the causal relation between two optical modes, and then show that the nature of this relation can be inferred from the observed correlations. Finally, I discuss applications of this work and future directions. Based on: K. Ried, M. Agnew, L. Vermeyden, D. Janzing, R. W. Spekkens and K. J. Resch, Nature Physics (2015).