  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 can not be derived by any other means.

Soft Condensed Matter;Statistical Mechanics;Biological Physics;Chemical Physics