  In the framework of mean-field based transport approaches, we discuss recent
results concerning heavy ion reactions between charge asymmetric systems, from
low up to intermediate energies. We focus on isospin sensitive observables,
aiming at extracting information on the density dependence of the isovector
part of the nuclear effective interaction and of the nuclear symmetry energy.
For reactions close to the Coulomb barrier, we explore the structure of
collective dipole oscillations, rather sensitive to the low-density behavior of
the symmetry energy. In the Fermi energy regime, we investigate the interplay
between dissipation mechanisms, fragmentation and isospin effects. At
intermediate energies, where regions with higher density and momentum are
reached, we discuss collective flows and their sensitivity to the momentum
dependence of the isovector interaction channel, which determines the splitting
of neutron and proton effective masses. Finally, we also discuss the isospin
effect on the possible phase transition from nucleonic matter to quark matter.
Results are critically reviewed, also trying to establish a link, when
possible, with the outcome of other transport models.
