Einstein's last untested prediction, the existence of gravitational waves, will soon be directly verified, for the first time, by advanced ground-based interferometers, such as advanced LIGO and Virgo.The most interesting gravitational wave science, however, will occur after the excitement of the first detection subsides and we begin to ask what new physical information can be gained with these observations. In this talk, I will focus on the nuclear physics information that we hope to acquire with gravitational waves emitted in the late binary inspiral of neutron stars. I will begin by discussing how the equation of state of supranuclear matter encodes itself in gravitational waves. I will then continue by describing the recently-discovered I-Love-Q relations (a mathematical correspondence between the moment of inertia, the Love number and the quadrupole moment of neutron stars) and how these help break degeneracies in gravitational wave data analysis. I will finally conclude by summarizing what nuclear physics information can be extracted from these gravitational waves.