  Giant resonances encapsulate the dynamic response of the nuclear ground state
to external perturbations. As such, they offer a unique view of the nucleus
that is often not accessible otherwise. Although interesting in their own
right, giant resonances are also enormously valuable in providing stringent
constraints on the equation of state of asymmetric matter. We this view in
mind, we focus on two modes of excitation that are essential in reaching this
goal: the isoscalar giant monopole resonance (GMR) and the isovector giant
dipole resonance (GDR). GMR energies in heavy nuclei are sensitive to the
symmetry energy because they probe the incompressibility of neutron-rich
matter. Unfortunately, access to the symmetry energy is hindered by the
relatively low neutron-proton asymmetry of stable nuclei. Thus, the measurement
of GMR energies in exotic nuclei is strongly encouraged. In the case of the
GDR, we find the electric dipole polarizability of paramount importance.
Indeed, the electric dipole polarizability appears as one of two laboratory
observables -- with the neutron-skin thickness being the other -- that are
highly sensitive to the density dependence of the symmetry energy. Finally, we
identify the softness of skin and the nature of the pygmy resonance as
important unsolved problems in nuclear structure.
