When two black holes inspiral and merge, they emit gravitational waves that have famously been detected for the first time by LIGO in 2015 . These gravitational waves carry energy as well as momentum away from the black-hole binary system. The energy loss is responsible for the inspiral and eventual merger. The linear momentum radiated away, on the other hand, can impart a recoil on the black-hole system, just like the firing of a bullet imparts a recoil on the shooter. This effect follows from conservation of momentum; for black holes, the gravitational waves carry net momentum in some direction, so the black-hole emitter has to respond by moving accordingly in the opposite direction.
One of the most dramatic results of numerical relativity has been the discovery of “superkicks”, very large recoil velocities of up to 3,700 km/s that occur when the black holes start their inspiral with specific spin directions [2,3]. Such large kicks are sufficient to eject black holes from even the most massive host galaxies; the escape velocities from giant elliptic galaxies are about 1,000 km/s. This has sparked a lot of interest among astrophysical observers to look for ejected black holes, because this would have major implications for the formation history of supermassive black holes. Several candidates have been found but alternative explanations (without resorting to kicks) cannot be ruled out; see  for a review.
As part of our DiRAC project, we have found that even larger recoil velocities, up to 4,300 km/s are realized when the black holes inspiral on moderately eccentric (rather than quasi-circular) orbits. In general, moderate eccentricity can amplify the recoil effect by up to 25% with possible effects on the retention rate of black holes in globular clusters, second-generation populations of black-hole merger events, as well as the black-hole occupation fraction of galaxies.
-  B. P. Abbott et al, Phys.Rev.Lett. 116 (2016) 061102, arXiv:1602.03837 [gr-qc]
-  J. A. Gonzalez et al, Phys.Rev.Lett. 98 (2007) 231101, gr-qc/0702052
-  M. Campanelli et al, Astrophys.J. 659 (2007) L5-L8, gr-qc/0701164
-  S. Komossa, Adv.Astron. 2012, 364073, arXiv:1202.1977 [astro-ph]
-  U. Sperhake et al, Phys.Rev.D 101 (2020) 024044 arXiv:1910.01598 [gr-qc]