1. A paradigm shift in Earth science -- 2. Encounters in space -- 3. Lunar impacts and the Late Heavy Bombardment (LHB) in the Earth-Moon system -- 4. Impact cratering and ejecta dynamics -- 5. Identification of impact structures -- 6. Impact ejecta and fallout units -- 7. Extraterrestrial geochemical, isotopic and mineralogical signatures -- 8. Precambrian asteroid impacts -- 9. Very large impact structures -- 10. Asteroid impact clusters and isotopic age peaks -- 11. Australian large asteroid impact and possible impact structures -- 12. Impacts and mass extinctions -- 13. Uniformitarian models and the role of asteroid impacts in Earth evolution -- 14. The current danger -- Index. When in 1981 Louis and Walter Alvarez, the father and son team, unearthed a tell-tale Iridium-rich sedimentary horizon at the 65 million years-old Cretaceous-Tertiary boundary at Gubbio, Italy, their find heralded a paradigm shift in the study of terrestrial evolution. Since the 1980s the discovery and study of asteroid impact ejecta in the oldest well-preserved terrains of Western Australia and South Africa, by Don Lowe, Gary Byerly, Bruce Simonson, the author and others, and the documentation of new exposed and buried impact structures in several continents, led to a resurgence of the idea of the catastrophism theory of Cuvier, earlier largely supplanted by the uniformitarian theory of Hutton and Lyell. Several mass extinction of species events are known to have occurred in temporal proximity to large asteroid impacts, global volcanic eruptions and continental splitting. Likely links are observed between asteroid clusters and at 580 Ma, end-Devonian, end-Triassic and end-Jurassic extinctions. New discoveries of ~3.5 Ga-old impact fallout units in South Africa have led Lowe and Byerly to propose a protracted continuation of the Late Heavy Bombardment (~3.95-3.85 Ga) in the Earth-Moon system. Given the difficulty in identifying asteroid impact ejecta units and buried impact structures, it is likely new discoveries of impact signatures are in store, which would further profoundly alter models of terrestrial evolution.