Supermassive black holes (SMBHs) may not always reside right at the centers of their host galaxies. This is a prediction of numerical relativity simulations, which imply that the newly formed single SMBH, after binary coalescence in a galaxy merger, can receive kick velocities up to several 1000 km/s due to anisotropic emission of gravitational waves. Long-lived oscillations of the SMBHs in galaxy cores, and in rare cases even SMBH ejections from their host galaxies, are the consequence. Observationally, accreting recoiling SMBHs would appear as quasars spatially and/or kinematically off-set from their host galaxies. The presence of the "kicks" has a wide range of astrophysical implications which only now are beginning to be explored, including consequences for black hole and galaxy assembly at the epoch of structure formation, black hole feeding, and unified models of Active Galactic Nuclei (AGN). Here, we review the observational signatures of recoiling SMBHs and the properties of the first candidates which have emerged, including follow-up studies of the candidate recoiling SMBH of SDSSJ092712.65+294344.0.