Properties of strongly interacting, two-component finite Fermi systems are discussed within the recently developed coordinate-space Hartree-Fock-Bogoliubov (HFB) approach. This approach is capable of treating the salient features of weakly bound and extremely deformed nuclei. I will talk about the nuclear quasi-particle continuum and resonances that can be precisely
described by the L2 discretization in a large box. Meanwhile, the numerical effects in solving the HFB equation on supercomputers are reviewed. I will also discuss the coordiante-space HFB approach to spin-polarized cold atomic gases, especially the Larkin-Ovchinnikov phase.