Bagui, EleniClesse, SébastienDe Luca, ValerioEzquiaga, Jose MaríaFranciolini, GabrieleGarcía-Bellido, JuanJoana, CristianKumar Jain, RajeevKuroyanagi, SachikoMusco, IliaPapanikolaou, TheodorosRaccanelli, AlviseRenaux-Petel, SébastienRiotto, AntonioRuiz Morales, EsterScalisi, MarcoSergijenko, OlgaÜnal, CanerVennin, VincentWands, David2025-03-172025-03-172025Primordial black holes and their gravitational-wave signatures / Eleni Bagui, Sébastien Clesse, Valerio De Luca, ... Olga Sergijenko [et al.] // Living Reviews in Relativity. - 2025. - Vol. 28. - Article number 1. - https://doi.org/10.1007/s41114-024-00053-w1433-8351https://doi.org/10.1007/s41114-024-00053-whttps://ekmair.ukma.edu.ua/handle/123456789/33975In 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, analyze 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.enblack holesprimordial black holescosmologygravitational wavesLISAarticleArticle