Twenty-two papers on tsunamis are included in the Pure and Applied Geophysicstopical issue Twenty five years of modern tsunami science following the 1992 Nicaragua and Flores Island tsunamis: Volume I, reporting on the frontiers of tsunami science and research. The first three papers overview significant tsunamis of 1992-2018 and discuss the problems of tsunami cataloguing. The main focus of the next four papers is on specific details of historical tsunami events and field surveys. First, three papers are related to thorough analyses of several historical events based on macroseismic, seismological, and tsunami observations, tide gauge data, and modelling results: the 1907 Sumatra tsunami earthquake, the 1941 Andaman Islands earthquake, and five great tsunamis in the Pacific Ocean (1946, 1952, 1957, 1960 and 1964). The last paper of the section concerns results of the field survey of the 2017 Bodrum-Kos tsunami. The reconstruction of the tsunami sources is the main target of the four following papers, with four events examined in detail: the historical 1810 Baja California, 1992 Flores Island, 2012 Haida Gwaii and 2015 Chilean (Illapel) tsunamis. A set of three papers address problems associated with landslide-generated tsunamis in three different regions: a modelling of the 2017 landslide and tsunami at Karrat Fjord, Greenland; a probabilistic analysis of the hazard from the Indus Canyon in the NW Indian Ocean; and a study of the landslide-induced tsunami hazard along the US East Coast. The next section, including three papers, reports on comparisons between different types of tsunami models, on numerical modelling of tsunami waves in the Caspian Sea, and on the modelling of magnetic signals at Easter Island, following the 2010 and 2015 Chilean tsunamis. The last group of five papers discusses tsunami hazard assessment and warning for various regions of the world oceans, including Alaska, the eastern and western Mediterranean, Australia, the Northeast Atlantic and the entire Pacific Ocean; one specific aspect of these studies is the compilation and efficient application of observed data, in particular, from DARTs.