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.

7 pages, 2 figures