Neutron stars provide a unique way to probe dense matter under extreme conditions, far beyond the reach of current terrestrial experiments. Although recent advances in nuclear theory or nuclear/heavy-ion collision experiments provide clues about the behaviour of dense matter, one must resort to theoretical models to extrapolate to unknown conditions relevant for neutron star interior. Recently the detection of gravitational waves has opened up a new window to the Universe beyond traditional multi-wavelength astronomy. In this talk, I present some of our recent investigations of how gravitational waves, in addition to astrophysical data and information from state-of-the-art terrestrial experiments, allow us to probe the interior composition of neutron stars.