The tragedy of the 2004 Indian Ocean tsunami has led to a rapid expansion in science directed at understanding tsunami and mitigating their hazard. A remarkable cross-section of this research was presented in the session: Tsunami Generation and Hazard, at the International Union of Geodesy and Geophysics XXIV General Assembly in Perugia, held in July of 2007. Over one hundred presentations were made at this session, spanning topics ranging from paleotsunami research, to nonlinear shallow-water theory, to tsunami hazard and risk assessment. A selection of this work, along with other contributions from leading tsunami scientists, is published in detail in the 28 papers of this special issue of Pure and Applied Geophysics: Tsunami Science Four Years After the Indian Ocean Tsunami. Part I of this issue includes 14 papers covering the state-of-the-art in tsunami modelling and hazard assessment. Another 14 papers are published in Part II focusing on observations and data analysis.