  We review recent progress in the theory of neutron matter with particular
emphasis on its superfluid properties. Results of quantum Monte Carlo
calculations of simple and realistic models of uniform superfluid neutron gas
are discussed along with those of neutrons interacting in a potential well
chosen to approximate neutron-rich oxygen isotopes. The properties of dilute
superfluid Fermi gases that may be produced in atom traps, and their relations
with neutron matter, are illustrated. The density dependence of the effective
interaction between neutrons, used to describe neutron-rich systems with the
mean field approximations, is also discussed.
