  Quantum networks have experienced rapid advancements in both theoretical and
experimental domains over the last decade, making it increasingly important to
understand their large-scale features from the viewpoint of statistical
physics. This review paper discusses a fundamental question: how can
entanglement be effectively and indirectly (e.g., through intermediate nodes)
distributed between distant nodes in an imperfect quantum network, where the
connections are only partially entangled and subject to quantum noise? We
survey recent studies addressing this issue by drawing exact or approximate
mappings to percolation theory, a branch of statistical physics centered on
network connectivity. Notably, we show that the classical percolation
frameworks do not uniquely define the network's indirect connectivity. This
realization leads to the emergence of an alternative theory called
``concurrence percolation,'' which uncovers a previously unrecognized quantum
advantage that emerges at large scales, suggesting that quantum networks are
more resilient than initially assumed within classical percolation contexts,
offering refreshing insights into future quantum network design.
