  We develop a description of fermionic superfluids in terms of an effective
field theory for the pairing order parameter. Our effective field theory
improves on the existing Ginzburg - Landau theory for superfluid Fermi gases in
that it is not restricted to temperatures close to the critical temperature.
This is achieved by taking into account long-range fluctuations to all orders.
The results of the present effective field theory compare well with the results
obtained in the framework of the Bogoliubov - de Gennes method. The advantage
of an effective field theory over Bogoliubov - de Gennes calculations is that
much less computation time is required. In the second part of the paper, we
extend the effective field theory to the case of a two-band superfluid. The
present theory allows us to reveal the presence of two healing lengths in the
two-band superfluids, to analyze the finite-temperature vortex structure in the
BEC-BCS crossover, and to obtain the ground state parameters and spectra of
collective excitations. For the Leggett mode our treatment provides an
interpretation of the observation of this mode in two-band superconductors.
