Abstract Tsunamis are unpredictable and infrequent but potentially large impact natural disasters. To prepare, mitigate and prevent losses from tsunamis, probabilistic hazard and risk analysis methods have been developed and have proved useful. However, large gaps and uncertainties still exist and many steps in the assessment methods lack information, theoretical foundation, or commonly accepted methods. Moreover, applied methods have very different levels of maturity, from already advanced probabilistic tsunami hazard analysis for earthquake sources, to less mature probabilistic risk analysis. In this review we give an overview of the current state of probabilistic tsunami hazard and risk analysis. Identifying research gaps, we offer suggestions for future research directions. An extensive literature list allows for branching into diverse aspects of this scientific approach. © Copyright © 2021 Behrens, Løvholt, Jalayer, Lorito, Salgado-Gálvez, Sørensen, Abadie, Aguirre-Ayerbe, Aniel-Quiroga, Babeyko, Baiguera, Basili, Belliazzi, Grezio, Johnson, Murphy, Paris, Rafliana, De Risi, Rossetto, Selva, Taroni, Del Zoppo, Armigliato, Bureš, Cech, Cecioni, Christodoulides, Davies, Dias, Bayraktar, González, Gritsevich, Guillas, Harbitz, Kânoǧlu, Macías, Papadopoulos, Polet, Romano, Salamon, Scala, Stepinac, Tappin, Thio, Tonini, Triantafyllou, Ulrich, Varini, Volpe and Vyhmeister. ; This article is based upon work from COST Action CA18109 AGITHAR, supported by COST (European Cooperation in Science and Technology). VB and PC obtained support through the VES20 Inter-Cost LTC 20020 project. MS-G obtained support through the Severo Ochoa Centers of Excellence Program (Ref. CEX 2018–000797-S). TU acknowledges funding from the European Union's Horizon 2020 research and innovation program (ChEESE project, Grant Agreement No. 823844).
