  The first detection of a binary neutron star merger through gravitational
waves and photons marked the dawn of multi-messenger astronomy with
gravitational waves, and it greatly increased our insight in different fields
of astrophysics and fundamental physics. However, many open questions on the
physical process involved in a compact binary merger still remain and many of
these processes concern plasma physics. With the second generation of
gravitational wave interferometers approaching their design sensitivity, the
new generation under design study, and new X-ray detectors under development,
the high energy Universe will become more and more a unique laboratory for our
understanding of plasma in extreme conditions. In this review, we discuss the
main electromagnetic signals expected to follow the merger of two compact
objects highlighting the main physical processes involved and some of the most
important open problems in the field.
