Tsunamis are multiscale phenomena resulting from a water column displacement that may be induced by multiple sources, and range from local scale inundation processes to ocean-wide scale wave propagation. Different strategies may be required to model tsunami evolution at different scales and to characterize various intensity measures. Research in tsunami hazard and risk has focused mostly on the tsunami effects such as the wave heights or flow depths. This chapter reviews the evolution of tsunami hazard and risk assessment methodologies, with particular emphasis on the development of probabilistic approaches. Building on advances in numerical modeling and uncertainty analysis, two main frameworks for Probabilistic Tsunami Hazard and Risk Analysis (PTHA/PTRA) are described. Framework 1 (FW1) focuses on quantitative methods, including fully simulation-based assessments (FW1A), integration of hazard with vulnerability and loss models (FW1B), consideration of dynamic processes such as tidal and sea-level variations (FW1C), and approaches using limited scenario sets (FW1D). Framework 2 (FW2) complements this by incorporating indicator-based vulnerability assessments, both physical (FW2A) and social, multi-dimensional (FW2B).