A variety of structural phenomena in exotic short-lived nuclei far from stability, especially in systems close to the particle drip lines, challenge model descriptions based on the self-consistent mean-field approximation. Because the Fermi level in a drip-line nucleus is very close to the continuum, both weakly-bound states and low-lying positive energy single-particle resonant states are essential to determine the A variety of structural phenomena in exotic short-lived nuclei far from stability, especially in systems close to the particle drip lines, challenge model descriptions based on the self-consistent mean-field approximation. Because the Fermi level in a drip-line nucleus is very close to the continuum, both weakly-bound states and low-lying positive energy single-particle resonant states are essential to determine the