  Binary neutron star mergers used to be the most promising candidate for
gravitational waves for ground-based gravitational wave detectors, such as
advanced LIGO and advanced VIRGO. This was proved by the detection of
gravitational waves from a binary neutron star merger in 2017. Numerical
modeling is pivotal in predicting and interpreting binary neutron star mergers.
This chapter reviews the progress of fully general relativistic magnetized
binary neutron star merger simulations. From 2008 to 2024, about forty
numerical relativity simulations of magnetized binary neutron star mergers were
conducted with a different level of sophistication. This chapter aims to
comprehensively view the magnetohydrodynamics effect in binary neutron star
mergers by reviewing all the related works.
