The dynamics of massive black holes (BHs) in galaxy mergers is a rich field of research that has seen much progress in recent years. In this contribution we briefly review the processes describing the journey of BHs during mergers, from the cosmic context all the way to when BHs coalesce. If two galaxies each hosting a central BH merge, the BHs would be dragged towards the center of the newly formed galaxy. If/when the holes get sufficiently close, they coalesce via the emission of gravitational waves. How often two BHs are involved in galaxy mergers depends crucially on how many galaxies host BHs and on the galaxy merger history. It is therefore necessary to start with full cosmological models including BH physics and a careful dynamical treatment. After galaxies have merged, however, the BHs still have a long journey until they touch and coalesce. Their dynamical evolution is radically different in gas-rich and gas-poor galaxies, leading to a sort of dichotomy between high-redshift and low-redshift galaxies, and late-type and early-type, typically more massive galaxies.
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