I will discuss experiments on the pairing of spin-polarized 6Li atoms in both 3D and 1D geometries. Spin-polarized ultracold atomic gases are excellent candidates for creating the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulated superfluid state. The FFLO state is characterized by pairs with non-zero center of mass momentum. In 3D, we find phase separation between a fully paired core and the surrounding unpaired atoms, but no evidence for the FFLO state. Theory predicts that FFLO is ubiquitous in 1D, however, and we have initiated a 1D experiment to verify these predictions. An array of one-dimensional tubes are formed by imposing a two-dimensional optical lattice on the atoms. We find that phase separation also occurs in 1D, but in contrast to 3D the central core is always partially polarized, while the outer wings are either fully paired or fully polarized, depending on the overall degree of spin polarization. The experimental phase diagram agrees well theory. Although not directly observed in the experiment, theory predicts that the partially polarized phase is the FFLO state.