  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.
