Measuring higher-order photon correlations of faint quantum light: A short review

•As a tutorial review provides an overview on the experimental aspects in measuring photon correlations.•Highlights the practicality of the higher-order moments in quantum state classification and characterization.•Sums up the usage of the normalized moments with orders higher than two in quantum optics and brings together crucial experimental considerations.•Anchors the normalized higher-order moments as quantum optical characterization tools and emphasizes their importance in the state tomography.