We present a personal view on the current state of statistical mechanics of
Coulomb fluids with special emphasis on the interactions between
macromolecular surfaces, concentrating on the weak and the strong coupling
limits. Both are introduced for a (primitive) counterion-only system in the
presence of macroscopic, uniformly charged boundaries, where they can be
derived systematically. Later we show how this formalism can be generalized to
the cases with additional characteristic length scales that introduce new
coupling parameters into the problem. These cases most notably include
asymmetric ionic mixtures with mono- and multivalent ions that couple
differently to charged surfaces, ions with internal charge (multipolar)
structure and finite static polarizability, where weak and strong coupling
limits can be constructed by analogy with the counterion-only case and lead to
important new insights into their properties that cannot be derived by any
other means
