  This survey provides a unified discussion of multiple integrals, moments,
cumulants and diagram formulae associated with functionals of completely random
measures. Our approach is combinatorial, as it is based on the algebraic
formalism of partition lattices and M\"obius functions. Gaussian and Poisson
measures are treated in great detail. We also present several combinatorial
interpretations of some recent CLTs involving sequences of random variables
belonging to a fixed Wiener chaos.
