To understand why nuclear matter is stable, and thereby shed light on the limits of nuclear stability, is one of the overarching aims and intellectual challenges of basic research in nuclear physics and science. To relate the stability of matter to the underlying fundamental forces and particles of nature as manifested in nuclear matter, is central to present and planned rare isotope facilities. Important properties of nuclear systems, which can reveal information about these topics are for example masses, and thereby binding energies, and density distributions of nuclei. These are quantities which convey important information on the shell structure of nuclei, with their pertinent magic numbers and shell closures or the eventual disappearance of the latter away from the valley of stability. Neutron-rich nuclei are particularly interesting for the above endeavor. As a particular chain of isotopes becomes more and more neutron rich, one reaches finally the limit of stability, the so-called drip line, where one additional neutron makes the next isotopes unstable with respect to the previous ones. The appearance or not of magic numbers and shell structures, the formation of neutron skins and halos can thence be probed via investigations of quantities like the binding energy or the charge radii and neutron rms radii of neutron-rich nuclei. In this talk I will present some recent calculations on properties of neutron-rich isotopes towards their corresponding drip lines and point to new experiments and the excitements and challenges in the nuclear physics community. I will also try to outline present and future challenges to nuclear many-body theory and how to understand the above properties in terms of the underlying forces.