  We briefly review recent progress on ultracold atomic Fermi gases with
different types of synthetic spin-orbit coupling, including the one-dimensional
(1D) equal weight Rashba-Dresselhaus and two-dimensional (2D) Rasbha spin-orbit
couplings. Theoretically, we show how the single-body, two-body and many-body
properties of Fermi gases are dramatically changed by spin-orbit coupling. In
particular, the interplay between spin-orbit coupling and interatomic
interaction may lead to several long-sought exotic superfluid phases at low
temperatures, such as anisotropic superfluid, topological superfluid and
inhomogeneous superfluid. Experimentally, only the first type - equal weight
combination of Rasbha and Dresselhaus spin-orbit couplings - has been realized
very recently using a two-photon Raman process. We show how to characterize a
normal spin-orbit coupled atomic Fermi gas in both non-interacting and
strongly-interacting limits, using particularly momentum-resolved
radio-frequency spectroscopy. The experimental demonstration of a
strongly-interacting spin-orbit coupled Fermi gas opens a promising way to
observe various exotic superfluid phases in the near future.
