  The nuclear symmetry energy at densities above saturation density
($\rho_0\sim 0.16 fm^{-3}$) is poorly constrained theoretically and very few
relevant experimental data exist. Its study is possible through Heavy Ion
Collisions (HIC) at energies $E/A> 200$ MeV, particularly with beams of
neutron-rich radioactive nuclei. The energy range implies that the momentum
dependence of the isospin fields, i.e. the difference of the effective masses
on protons and neutrons, also has to be investigated before a safe constraint
on $\esy(\rho)$ is possible. We discuss the several observables which have been
suggested, like $n/p$ emission and their collective flows and the ratio of
meson yields with different isospin projection, $\pi^-/\pi^+$ and $K^0/K^+$. We
point out several physical mechanisms that should be included in the
theoretical models to allow a direct comparison to the more precise experiments
which will be able to distinguish the isospin projection of the detected
particles: CSR/Lanzhou, FAIR/GSI, RIBF/RIKEN, FRIB/MSU.
