This page is still in progress.
Photon correlations
The pillar of quantum optics. It is typically measured with Glauber's $g^{(2)}$.
Bunching
The historical starting point through the Hanbury Brown-Twiss effect that describes the tendency of bosons to be detected together.
Antibunching
Superbunching
Multidimensional correlations
...involving time and space or time and spatial frequency dimensions...
Metrology
References
A good review is given in Ref. [1].