  In nuclear collisions induced by stable or radioactive neutron-rich nuclei a
transient state of nuclear matter with an appreciable isospin asymmetry as well
as thermal and compressional excitation can be created. This offers the
possibility to study the properties of nuclear matter in the region between
symmetric nuclear matter and pure neutron matter. In this review, we discuss
recent theoretical studies of the equation of state of isospin-asymmetric
nuclear matter and its relations to the properties of neutron stars and
radioactive nuclei. Chemical and mechanical instabilities as well as the
liquid-gas phase transition in asymmetric nuclear matter are investigated. The
in-medium nucleon-nucleon cross sections at different isospin states are
reviewed as they affect significantly the dynamics of heavy ion collisions
induced by radioactive beams. We then discuss an isospin-dependent transport
model, which includes different mean-field potentials and cross sections for
the proton and neutron, and its application to these reactions. Furthermore, we
review the comparisons between theoretical predictions and available
experimental data. In particular, we discuss the study of nuclear stopping in
terms of isospin equilibration, the dependence of nuclear collective flow and
balance energy on the isospin-dependent nuclear equation of state and cross
sections, the isospin dependence of total nuclear reaction cross sections, and
the role of isospin in preequilibrium nucleon emissions and subthreshold pion
production.
