Abstract: We briefly review current research on strongly interacting ultracold atomic polarized Fermi gases. In three dimensions the ground state of such systems is under strong debate. To gain some insights we investigate a system of one-dimensional strongly interacting polarized Fermi gases. In free space this is an integrable system, and therefore an exact phase diagram can be obtained. We show that an inhomogeneous superfluid state is most widespread in the phase diagram. We consider also the trapped case with an external harmonic trap, where two novel phase separation phases are found using the local density approximation.