The recent first direct detection of gravitational and electromagnetic waves, emitted during the coalescence of two neutron stars, opens a new era of multi-messenger astronomy that will lead to important discoveries in several areas of physics. In this talk I will discuss some of them, namely (i) how to constraint the Equation of State of neutron star matter, (ii) how to confirm and improve our models of plasma physics and (iii) how to discern among different alternative theories of gravity.