The structure of galactic nuclei reflects the presence of supermassive black holes in many ways. Single SMBHs act as sinks, destroying a mass in stars equal to their own mass in roughly one relaxation time and forcing nuclei to expand. Binary SMBHs displace roughly their combined mass in stars, creating low-density cores and hyper-velocity stars. Ejection of coalesced binary SMBHs via radiation recoil injects further energy into nuclei and creates the possibility of substantially displaced SMBHs. I will review these and related processes and discuss the observational implications.