Twenty papers on the study of tsunamis are included in Volume III of the PAGEOPH topical issue “Global Tsunami Science: Past and Future”. Volume I of this topical issue was published as PAGEOPH, vol. 173, No. 12, 2016 and Volume II as PAGEOPH, vol. 174, No. 8, 2017. Two papers in Volume III focus on specific details of the 2009 Samoa and the 1923 northern Kamchatka tsunamis; they are followed by three papers related to tsunami hazard assessment for three different regions of the world oceans: South Africa, Pacific coast of Mexico and the northwestern part of the Indian Ocean. The next six papers are on various aspects of tsunami hydrodynamics and numerical modelling, including tsunami edge waves, resonant behaviour of compressible water layer during tsunamigenic earthquakes, dispersive properties of seismic and volcanically generated tsunami waves, tsunami runup on a vertical wall and influence of earthquake rupture velocity on maximum tsunami runup. Four papers discuss problems of tsunami warning and real-time forecasting for Central America, the Mediterranean coast of France, the coast of Peru, and some general problems regarding the optimum use of the DART buoy network for effective real-time tsunami warning in the Pacific Ocean. Two papers describe historical and paleotsunami studies in the Russian Far East. The final set of three papers importantly investigates tsunamis generated by non-seismic sources: asteroid airburst and meteorological disturbances. Collectively, this volume highlights contemporary trends in global tsunami research, both fundamental and applied toward hazard assessment and mitigation.