We discuss random matrix models in terms of elementary operations on B
lue's functions (functional inverse of Green's functions). We show tha
t such a description encapsulates the essence of a number of physical
phenomena whether at/or away from the critical points and provides an
elegant way for discussing them. We illustrate these assertions by bor
rowing on a number of recent results in effective QCD in vacuum and ma
tter, as well as effective quantum systems of disorder with strong or
weak dissipation (Hatano-Nelson localization).