We discussed several structure problems of nuclei both near the neutron and the proton drip lines. The conditions for the growth of halo nucleus are discussed together with experimental evidence of neutron and proton halos. Next, a microscopic Hartree-Fock (HF) + random phase approximation (RPA) model is applied to calculate dipole excitations in halo nuclei, and the results are compared with experimental data in 11Be. It is pointed out that the abnormally large dipole strength is accumulated by the threshold effect inherent to halo nuclei. Giant Gamow-Teller (GT) states in nuclei near the proton drip line is also studied by using the same microscopic model. The nuclei with Z28 are predicted to have giant GT beta decays which carry most of the sum rule strength.