The massive Galactic black hole and the stars around it are a unique laboratory for studying how relaxation processes lead to close interactions of stars and compact remnants with the central massive black hole, in particular those leading to the emission of gravitational waves. I review new results on the processes of strong mass segregation and loss-cone refilling by massive perturbers and resonant relaxation; describe observational evidence that these processes play a role in the Galactic Center and can be studied there; and discuss some of the implications for Extreme Mass Ration Inspiral event rates and their properties.