The “magic” word complexity evokes a multitude of meanings that obscure its real sense. Here we try and generate a bottom-up reconstruction of the deep sense of complexity by looking at the convergence of different features shared by complex systems. We specifically focus on complexity in biology but stressing the similarities with analogous features encountered in inanimate and artefactual systems in order to track an integrative path toward a new “mainstream” of science overcoming the actual fragmentation of scientific culture.