  Topological Fermi superfluids have played the central role in various fields
of physics. However, all previous studies focus on the cases where Cooper pairs
have zero center-of-mass momenta (i.e. normal superfluids). The topology of
Fulde-Ferrell superfluids with nonzero momentum pairings have never been
explored until recent findings that Fulde-Ferrell superfluids in a spin-orbit
coupled Fermi gas can accommodate Majorana fermions in real space in low
dimensions and Weyl fermions in momentum space in three dimension. In this
review, we first discuss the mechanism of pairings in spin-orbit coupled Fermi
gases in optical lattices subject to Zeeman fields, showing that spin-orbit
coupling as well as Zeeman fields enhance Fulde-Ferrell states while suppress
Larkin-Ovchinnikov states. We then present the low temperature phase diagram
including both FF superfluids and topological FF superfluids phases in both two
dimension and three dimension. In one dimension, Majorana fermions as well as
phase dependent order parameter are visualized. In three dimension, we show the
properties of Weyl fermions in momentum space such as anisotropic linear
dispersion, Fermi arch, and gaplessness away from $k_{\perp}=0$. Finally, we
discuss some possible methods to probe FF superfluids and topological FF
superfluids in cold atom systems.
