  The isospin dependence of in-medium nuclear effective interactions is a
fundamental issue in nuclear physics and has broad ramifications in
astrophysics. Its uncertainties, especially the difference of neutron-proton
interactions in the isosinglet and isotriplet channels, affect significantly
the density and momentum dependence of the isovector single-nucleon potential
and nucleon-nucleon short-range correlation in neutron-rich matter.
Consequently, the neutron-proton effective mass splitting and the density
dependence of nuclear symmetry energy are still rather uncertain. Heavy-ion
reactions especially those involving rare isotopes is a useful tool for probing
the isospin dependence of nuclear effective interactions through (1) the
neutron-skin in coordinate and proton-skin in momentum of the initial state of
colliding nuclei, (2) the density and momentum dependence of especially the
isovector nuclear mean-field as well as (3) the isospin dependence of in-medium
nucleon-nucleon cross sections. Observations of neutron stars especially since
GW1710817 have also helped us significantly in understanding the isospin
dependence of nuclear effective interactions. {\it We summarize here a review
talk on these issues given at the 2021 International Workshop on multi-facets
of EOS and Clustering. For details we refer the readers to the original
publications and references therein}.
