  Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium
nuclear interaction in regions away from saturation. In this report we present
a selection of new reaction observables in dissipative collisions particularly
sensitive to the symmetry term of the nuclear Equation of State (Iso-EoS). We
will first discuss the Isospin Equilibration Dynamics. At low energies this
manifests via the recently observed Dynamical Dipole Radiation, due to a
collective neutron-proton oscillation with the symmetry term acting as a
restoring force. At higher beam energies Iso-EoS effects will be seen in
Imbalance Ratio Measurements, in particular from the correlations with the
total kinetic energy loss. For fragmentation reactions in central events we
suggest to look at the coupling between isospin distillation and radial flow.
In Neck Fragmentation reactions important $Iso-EoS$ information can be obtained
from the correlation between isospin content and alignement. The high density
symmetry term can be probed from isospin effects on heavy ion reactions at
relativistic energies (few AGeV range). Rather isospin sensitive observables
are proposed from nucleon/cluster emissions, collective flows and meson
production. The possibility to shed light on the controversial neutron/proton
effective mass splitting in asymmetric matter is also suggested. A large
symmetry repulsion at high baryon density will also lead to an "earlier"
hadron-deconfinement transition in n-rich matter. A suitable treatment of the
isovector interaction in the partonic EoS appears very relevant.
