  (Review) Properties of neutral and charged anyon fluids are examined, with
the main focus on the question whether or not a charged anyon fluid exhibits a
superconductivity at zero and finite temperature. Quantum mechanics of anyon
fluids is precisely described by Chern-Simons gauge theory. The random phase
approximation (RPA), the linearized self-consistent field method (SCF), and the
hydrodynamic approach employed in the early analysis of anyon fluids are all
equivalent. Relations and differences between neutral and charged anyon fluids
are discussed. It is necessary to go beyond RPA and the linearized SCF, and
possively beyond the Hartree-Fock approximation, to correctly describe various
phenomena such as the flux quantization, vortex formation, and phase
transition.
  Topics includes: Anyons, Aharonov-Bohm effect, Chern-Simons gauge theory,
Hartree-Fock ground state, RPA and SCF, Path integral representation, RPA =
linearized SCF, Response functions, Phonons and plasmons, Hydrodynamic
description, Effective theory, Meissner effect at zero and finite temperature,
de Haas - van Alphen effect in SCF, Thermodynamic potential in inhomogeneous
fields, T_c, Other important issues. (To appear in Int. J. Mod. Phys. B)
