  We review some recent progresses on the study of ultracold Fermi gases with
synthetic spin-orbit coupling. In particular, we focus on the pairing
superfluidity in these systems at zero temperature. Recent studies have shown
that different forms of spin-orbit coupling in various spatial dimensions can
lead to a wealth of novel pairing superfluidity. A common theme of these
variations is the emergence of new pairing mechanisms which are direct results
of spin-orbit-coupling-modified single-particle dispersion spectra. As
different configurations can give rise to single-particle dispersion spectra
with drastic differences in symmetry, spin dependence and low-energy density of
states, spin-orbit coupling is potentially a powerful tool of quantum control,
which, when combined with other available control schemes in ultracold atomic
gases, will enable us to engineer novel states of matter.
