  Neutron stars (NSs) are compact objects that host the densest forms of matter
in the observable universe, providing unique opportunities to study the
behaviour of matter at extreme densities. While precision measurements of NS
masses through pulsar timing have imposed effective constraints on the equation
of state (EoS) of dense matter, accurately determining the radius or moment of
inertia (MoI) of a NS remains a major challenge. This article presents a
detailed review on measuring the Lense-Thirring (LT) precession effect in the
orbit of binary pulsars, which would give access to the MoI of NSs and offer
further constraints on the EoS. We discuss the suitability of certain classes
of binary pulsars for measuring the LT precession from the perspective of
binary star evolution, and highlight five pulsars that exhibit properties
promising to realise these goals in the near future. Finally, discoveries of
compact binaries with shorter orbital periods hold the potential to greatly
enhance measurements of the MoI of NSs. The MoI measurements of binary pulsars
are pivotal to advancing our understanding of matter at supranuclear densities
as well as improving the precision of gravity tests, such as the orbital decay
due to gravitational wave emission and of tests of alternative gravity
theories.
