  A central question for causal inference is to decide whether a set of
correlations fit a given causal structure. In general, this decision problem is
computationally infeasible and hence several approaches have emerged that look
for certificates of compatibility. Here we review several such approaches based
on entropy. We bring together the key aspects of these entropic techniques with
unified terminology, filling several gaps and establishing new connections
regarding their relation, all illustrated with examples. We consider cases
where unobserved causes are classical, quantum and post-quantum and discuss
what entropic analyses tell us about the difference. This has applications to
quantum cryptography, where it can be crucial to eliminate the possibility of
classical causes. We discuss the achievements and limitations of the entropic
approach in comparison to other techniques and point out the main open
problems.
