  The field of nuclear science has considerably advanced since its beginning
just over a century ago. Today, the science of rare isotopes is on the cusp of
a new era with theoretical and computing advances complementing experimental
capabilities at new facilities internationally. In this article we present a
vision for the science of rare isotope beams (RIBs). We do not attempt to cover
the full breadth of the field, but rather provide a perspective and address a
selection of topics that reflect our own interests and expertise. We focus in
particular on systems near the drip lines, where one often finds nuclei that
are referred to as "exotic," and where the role of the "nuclear continuum" is
only just starting to be explored. An important aspect of this article is the
attempt to highlight the crucial connections between nuclear structure and
nuclear reactions required to fully interpret and leverage the rich data to be
collected in the next years at RIB facilities. Further, we connect the efforts
in structure and reactions to key questions of nuclear astrophysics.
