It is a remarkable fact that information on the equation of state of nuclear matter can be obtained from the analysis of gravitational waves emitted in the inspiral and merger of binary neutron stars. Moreover, information on the equation of state of this cold, dense nuclear matter cannot be obtained from experiments in particle accelerators, and must rely on neutron star data. For example, the tidal deformability of the stars (which depends on the equation of state) can modify the expected gravitational wave signal right before the merger. I will describe the current results from recent observations and also discuss how the characteristic modes of oscillation of neutron stars, which can be excited in close passages of eccentric binaries or after the merger, will also bring clear information on the stellar composition, as a consequence of the universal relations satisfied by the frequencies.