  Causal reasoning is essential to science, yet quantum theory challenges it.
Quantum correlations violating Bell inequalities defy satisfactory causal
explanations within the framework of classical causal models. What is more, a
theory encompassing quantum systems and gravity is expected to allow causally
nonseparable processes featuring operations in indefinite causal order, defying
that events be causally ordered at all. The first challenge has been addressed
through the recent development of intrinsically quantum causal models, allowing
causal explanations of quantum processes -- provided they admit a definite
causal order, i.e. have an acyclic causal structure. This work addresses
causally nonseparable processes and offers a causal perspective on them through
extending quantum causal models to cyclic causal structures. Among other
applications of the approach, it is shown that all unitarily extendible
bipartite processes are causally separable and that for unitary processes,
causal nonseparability and cyclicity of their causal structure are equivalent.
