We review some relations occurring between the combinatorial
intersection theory on the moduli spaces of stable curves and the
asymptotic behavior of the 't Hooft-Kontsevich matrix integrals.
In particular, we give an alternative proof of the
Witten-Di~Francesco-Itzykson-Zuber theorem ---which expresses
derivatives of the partition function of intersection numbers as
matrix integrals--- using techniques based on diagrammatic calculus
and combinatorial relations among intersection numbers. These
techniques extend to a more general interaction potential.