The nuclear many-body Hamiltonian is supposed to describe all nuclei that can exist and not merely one nucleus of a given number of protons and neutrons. In this sense, a nucleus is never closed, isolated quantum system but communicates with other nuclei through virtual excitations, decay and captures. The communication is broken and the nucleus becomes artificially closed if the subspace of continuum states is excluded in the network of coupled systems. Obviously, the closed quantum system idealization of a real many-body system has very different features from those observed, in particular in the neighborhood of each reaction threshold. Impressive progress has been achieved over last few years in the development of shell model for weakly bound or unbound nuclear states. The real-energy continuum shell model (the so- called Shell Model Embedded in the Continuum) has been extended to treat the two-particle continuum and applied for the description of two-proton radioactivity. The shell model in the complex k-plane (the so-called Gamow Shell Model (GSM)) has been formulated using a complex Berggren ensemble and applied for binding energies and energy spectra of bound and unbound neutron-rich helium and lithium isotopes, spin-orbit splittings and spectroscopic factors. In this framework, we shall discuss recent results involving spectra, p-capture reaction cross- sections, binding systematics, spectroscopic factors and the one-neutron overlap integrals for neutron-rich drip-line nuclei. Moreover, salient features of level degeneracies in both integrable and non-integrable open quantum systems will also be discussed.