It is generally acknowledged that an extrapolation in physics from a
well-known scale to an unknown scale is perilous. This prevents us from using
laboratory experience to gain precise information for the supranuclear matter
inside neutron stars (NSs). With operating and upcoming astronomical
facilities, NSs' equation of state (EOS) is expected to be determined at a new
level in the near future, under the assumption that general relativity (GR) is
the correct theory for gravitation. While GR is a reasonable working assumption
yet still an extrapolation, there could be a large uncertainty due to the
not-so-well-tested strong gravitational field inside NSs. Here we review some
recent theoretical efforts towards a better understanding of the degeneracy
between the supranuclear EOS and alternative gravity theories.Comment: 11 pages, 6 figure