The BCS theory explains conventional superconductivity in terms of electrons with opposite spin and momentum that condense into pairs. A sufficiently large magnetic field destroys superconductivity by coupling to the orbital motion of the electrons. In 1964, Fulde & Ferrell and Larkin & Ovchinnikov (FFLO) showed that this coupling would give rise to a state different to the conventional BCS-state. In particular, this state may exhibit a spatially modulated order parameters as well as finite momentum of Cooper pairs. Up to now, the FFLO state is still elusive to experimental observation. In the talk, I will discuss our theoretical studies on the FFLO states of polarized fermions in cold atoms and condensed matter systems. First we investigate the superfluidity with imbalanced populations of harmonically trapped ultracold fermions in a 2D optical lattice. In the high-density regime, a novel FFLO state with gap oscillation along the angular direction shows up and the accompanying ferromagnetic order modulates accordingly. Next we study the electronic properties of a heterostructure consisting of ferromagnetic metallic layer and s-wave superconductor layer. We demonstrate that a novel stripe FFLO state as well as a 2D FFLO state may show up due to the proximity effect.