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.

We present a depth-integrated equation for the mechanics of propagation of lowfrequency\ud hydroacoustic waves due to a sudden bottom displacement associated with\ud earthquakes. The model equation can be used for numerical prediction in large-scale\ud domains, overcoming the computational difficulties of three-dimensional models and so\ud creating a solid base for tsunami early warning systems

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