  Various kinds of isovector nucleon effective masses are used in the
literature to characterize the momentum/energy dependence of the nucleon
symmetry potential or self-energy due to the space/time non-locality of the
underlying isovector strong interaction in neutron-rich nucleonic matter. The
multifaceted studies on nucleon isovector effective masses are
multi-disciplinary in nature. Besides structures, masses and low-lying excited
states of nuclei as well as nuclear reactions, studies of the isospin
dependence of short-range correlations in nuclei from scatterings of
high-energy electrons and protons on heavy nuclei also help understand nucleon
effective masses especially the so-called E-mass in neutron-rich matter. A
thorough understanding of all kinds of nucleon effective masses has multiple
impacts on many interesting issues in both nuclear physics and astrophysics. We
review some of the significant progresses made in recent years by the nuclear
physics community in resolving some of the hotly debated and longstanding
issues regarding nucleon effective masses especially in dense neutron-rich
matter.
