Most tsunamis are generated by earthquakes, but in 1998, a seabed slump offshore of northern Papua New Guinea (PNG) generated a tsunami up to 15 m high that killed more than 2,200 people. The event changed our understanding of tsunami mechanisms and was forerunner to two decades of major tsunamis that included those in Turkey, the Indian Ocean, Japan, and Sulawesi and Anak Krakatau in Indonesia. PNG provided a context to better understand these tsunamis as well as older submarine landslide events, such as Storegga (8150 BP); Alika 2 in Hawaii (120,000 BP), and Grand Banks, Canada (1929), together with those from dual earthquake/landslide mechanisms, such as Messina (1908), Puerto Rico (1928), and Japan (2011). PNG proved that submarine landslides generate devastating tsunamis from failure mechanisms that can be very different, whether singly or in combination with earthquakes. It demonstrated the critical importance of seabed mapping to identify these mechanisms as well as stimulated the development of new numerical tsunami modeling methodologies. In combination with other recent tsunamis, PNG demonstrated the critical importance of these events in advancing our understanding of tsunami hazard and risk. This review recounts how, since 1998, understanding of the tsunami hazard from submarine landslides has progressed far beyond anything considered possible at that time. ▪ For submarine landslide tsunamis, advances in understanding take place incrementally, usually in response to major, sometimes catastrophic, events. ▪ The Papua New Guinea tsunami in 1998, when more than 2,200 people perished, was a turning point in first recognizing the significant tsunami hazard from submarine landslides. ▪ Over the past 2 to 3 years advances have also been made mainly because of improvements in numerical modeling based on older tsunamis such as Grand Banks in 1929, Messina in 1908, and Storegga at 8150 BP. ▪ Two recent tsunamis in late 2018, in Sulawesi and Anak Krakatau, Indonesia, where several hundred people died, were from very unusual landslide mechanisms—dual (strike-slip and landslide) and volcanic collapse—and provide new motivations for understanding these tsunami mechanisms. ▪ This is a timely, state of the art review of landslide tsunamis based on recent well-studied events and new research on older ones, which provide an important context for the recent tsunamis in Indonesia in 2018. Expected final online publication date for the Annual Review of Earth and Planetary Sciences, Volume 49 is May 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.