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At low redshift, massive black holes are found in the centers of almost all large elliptical galaxies, and also in many lower-mass systems. Their evolution is believed to be inextricably entangled with that of their host galaxies. On the one hand, the galactic environment provides gas for the black holes to grow via accretion and shine as active galactic nuclei. On the other hand, massive black holes are expected to backreact on the galactic dynamics, by injecting energy in their surroundings via jets or radiative feedback. Moreover, if galaxies and dark-matter halos form hierarchically, from small systems at high redshift coalescing into larger ones at more recent epochs, massive black holes may also merge, potentially generating gravitational-wave signals detectable by present and future experiments. In this Chapter, we discuss the predictions of current astrophysical models for the mergers of massive black holes in the mHz frequency band of the Laser Interferometer Space Antenna (LISA) and in the nHz frequency band of pulsar-timing array experiments. We focus in particular on the astrophysical uncertainties affecting these predictions, including the poorly known dynamical evolution of massive black hole pairs at separations of hundreds of parsecs; the possible formation of 'stalled' binaries at parsec separations ('final-parsec problem'); and the effect of baryonic physics (e.g. SN feedback) on the growth of massive black holes. We show that nHz-band predictions are much more robust than in the mHz band, and comment on the implications of this fact for LISA and pulsar-timing arrays.