A variety of dynamical processes shapes the density of stars and gas in our Galactic center. We emphasize the role of binary stars dissolving in the tidal field of the super massive black hole. These are thought to produce hypervelocity stars, which are observed to escape our Galaxy. We show that they also play a role in setting the stellar cusp around the central black hole. Stars emitting gravitational waves spiral slowly toward the black hole, and once close enough transfer mass to it.We discuss the gravitational wave signal emitted and show that it may reflect internal properties of the star. Dissolving binaries may influence the rate of such events as compared to more violent stellar deaths in tidal disruption events.