  Massive black holes (MBHs), with masses in the range 10^3-10^8 Msolar, which
merge with a companion black hole of similar mass are expected to be the most
powerful source of gravitational radiation in the frequency range probed by
LISA. MBH binaries can be detected by LISA up to z~5-15. Gravitational waves
from MBH mergers can serve as a powerful tool to study the early evolution of
the MBH population, and possibly the role played by MBHs in the joint evolution
with their hosts. I review scenarios for the co-evolution of MBHs and
cosmological structures, where MBH seeds form in pre-galactic structures. These
black holes evolve then in a hierarchical fashion, following the merger
hierarchy of their hosts. Accretion of gas, traced by quasar activity, plays a
fundamental role in determining the two parameters defining a black hole, mass
and spin. Gravitational waves, together with observations in electromagnetic
bands, can help constrain the evolution of both MBH mass and spin.
