Studying neutron stars and dense matter with gravitational waves

Detections of neutron stars in binaries through gravitational waves offer a novel way to probe the properties of extremely dense matter. In this talk I will describe the properties of the signals we have observed, what they have already taught us, and what we expect to learn in the future. I will also discuss how information from gravitational waves can be combined and compared against other astrophysical and terrestrial probes of neutron star matter to unveil to the properties of the most dense material objects that we know of.