We are now living a new era of development of nuclear sciences thanks to the discovery of exotic or unstable nuclei. The Odyssey to reach the limits of stability is pushing nuclear sciences to unexpected discoveries and to a redefinition of its scope and methods. This is a step-by-step revolution that is both experimentally and theoretically a scientific challenge and an exciting cultural progress. The description of unstable systems requires a reconsideration of the role of the continuum that increases its importance near the drip-lines. Typically by moving from the valley of stability outward, the bound excited states of the stable nucleus are shifted to the continuum, forming low-lying resonances. The coupling to these states becomes of fundamental importance for the description of nuclear reactions. At the same time the coupling to non-resonant continuum states becomes more relevant. The 'file rouge' of the present thesis is to link different aspects of the complexity of the continuum spectrum in nuclear structure and nuclear reactions involving both stable and unstable nuclei either as tools or as subject of our study.