Two recent tsunamis, associated with the 2004 Sumatra–Andaman and 2011 Tohoku earthquakes, caused the worst tsunami disasters in the world. Other examples of recent, historical, and prehistoric tsunamis are also introduced. Tsunami observation systems include instrumental measurements, field surveys of tsunami-related damage and tsunami heights, and studies that utilize historical and geologic data, determine the magnitude of a tsunami, and develop catalogs. Tsunami generation due to earthquake faulting, landslides, and volcanic eruptions is discussed. The inverse modeling of tsunami generation is also described. Methods of evaluating tsunami propagation with its hydrodynamic background and numerical computations are introduced. Practical applications include the basin-wide and local tsunami warning systems, as well as tsunami disaster mitigations, such as hazard maps or probabilistic hazard assessments.