In the recent years, primordial black holes (PBHs) have emerged as one of the
most interesting and hotly debated topics in cosmology. Among other
possibilities, PBHs could explain both some of the signals from binary black
hole mergers observed in gravitational wave detectors and an important
component of the dark matter in the Universe. Significant progress has been
achieved both on the theory side and from the point of view of observations,
including new models and more accurate calculations of PBH formation,
evolution, clustering, merger rates, as well as new astrophysical and
cosmological probes. In this work, we review, analyse and combine the latest
developments in order to perform end-to-end calculations of the various
gravitational wave signatures of PBHs. Different ways to distinguish PBHs from
stellar black holes are emphasized. Finally, we discuss their detectability
with LISA, the first planned gravitational-wave observatory in space.Comment: 161 pages, 47 figures, comments welcom