We discuss a least-action principle characterizing ensemble-averages i
n statistical dynamics, based upon ''effective actions'' defined as in
quantum field-theory. These generalize to all system variables the On
sager-Machlup actions of thermodynamic fluctuation theory. In the stat
istical steady-state, the variational principles discussed are related
to the ''thermodynamical formalism'' for chaotic dynamical systems. N
on-perturbative methods of field-theory can be applied to approximate
the effective actions: instantons, 1/N-expansion, Hartree-Fock, Raylei
gh-Ritz, etc. In particular, the Rayleigh-Ritz method is shown to be c
losely related to traditional moment-closure schemes. Some concrete ap
plications of the variational methods are outlined, e.g., to free deca
y of homogeneous, isotropic Navier-Stokes turbulence at high Reynolds
number. ''Fluctuation-dissipation relations'' are obtained for the str
ength of turbulence-generated eddy noise in terms of mean dissipation
Characteristics. The relation of the effective action to dissipation a
nd transport characteristics was already noted by Onsager, who pointed
out that the associated variational principles generalize the hydrody
namic least-dissipation principle of Rayleigh. We briefly discuss the
application of such principles to pattern-selection far from equilibri
um.