  A polarized ep/eA collider (Electron-Ion Collider, or EIC) with variable
center-of-mass energy sqrt(s) ~ 20-70 GeV and a luminosity ~ 10^{34} cm^{-2}
s^{-1} would be uniquely suited to address several outstanding questions of
Quantum Chromodynamics (QCD) and the microscopic structure of hadrons and
nuclei: (i) the three-dimensional structure of the nucleon in QCD (sea quark
and gluon spatial distributions, orbital motion, polarization, correlations);
(ii) the fundamental color fields in nuclei (nuclear parton densities,
shadowing, coherence effects, color transparency); (iii) the conversion of
color charge to hadrons (fragmentation, parton propagation through matter,
in-medium jets). We briefly review the conceptual aspects of these questions
and the measurements that would address them, emphasizing the qualitatively new
information that could be obtained with the collider. Such a medium-energy EIC
could be realized at Jefferson Lab after the 12 GeV Upgrade (MEIC), or at
Brookhaven National Lab as the low-energy stage of eRHIC.
