  The realizations of spin-orbit coupling in cold atoms lead to a burst of
research activities in the searching of topological matters in ultracold atom
systems. The very recent theoretical predictions show that topological
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids can be realized with proper
spin-orbit coupling and Zeeman fields. In this work, a comprehensive
understanding of the pairing symmetry, phase diagram and the edge modes in this
new topological matter are presented. The momentum of the Cooper pairs plays
the role of renormalizing the in-plane Zeeman field and chemical potential. The
in-plane Zeeman field and finite momentum pairing induce asymmetry to the
effective $p$-wave pairing, apart from a small fraction of higher orbital
components. The phase diagram is composed by different phases, which are
determined by the topology and band gap nature of the superfluids. Especially,
the gapped and gapless topological FFLO phase have totally different finite
size effect. These novel features show that the spin-orbit coupled cold atoms
provides an important platform in realizing topological matters which may not
be materialized with solids.
