From ancient times through to the Renaissance reports of stones, fragments of iron and ‘six hundred other things’ fallen from the sky were written down in books. With few exceptions, these were taken as signals of heaven's wrath. The 18th century Enlightenment brought an entirely new approach in which savants sought rational explanations, based on the laws of physics, for unfamiliar phenomena. They accepted Isaac Newton's dictum of 1718 that outer space must be empty in order to perpetuate the laws of gravitation, and, at the same time, they rejected an old belief that stones can coalesce within the atmosphere. Logically, then, nothing could fall from the skies, except ejecta from volcanoes or objects picked up by hurricanes. They dismissed reports of fallen stones or irons as tales told by superstitious country folk, and ascribed stones with black crusts to bolts of lightning on pyritiferous rocks. The decade between 1794 and 1804 witnessed a dramatic advance from rejection to acceptance of meteorites. The three main contributing factors were E.F.F. Chladni's book of 1794, in which he argued for the actuality of falls and linked them with fireballs; the occurrence of four witnessed and widely publicized falls of stones between 1794 and 1798; and chemical and mineralogicai analyses of stones and irons, published in 1802 by Edward C. Howard and Jacques-Louis de Bournon. They showed that stones with identical textures and compositions, very different from those of common rocks, have fallen at different times in widely separated parts of the world. They also showed that erratic masses of metallic iron and small grains of iron in the stones both contain nickel, so they must share a common origin. Meanwhile, in 1789, Anton-Laurent de Lavoisier had revived the idea of the accretion of stones within the atmosphere, which became widely accepted. Its chief rival was a hypothesis that fallen stones were erupted by volcanoes on the Moon. During the first half of the 19th century falls of carbonaceous chondrites and achondrites, and observations on the metallography of irons, provided fresh insights on the range of compositions of meteorite parent bodies. By 1860 both of the two main hypotheses of origins were abandoned, and debates intensified on whether all meteorites were fragments of asteroids or some of them originated in interstellar space. This paper will trace some of the successes and some of the failures that marked the efforts to gain a better understanding of meteorite falls from the end of the 15th century to the early 20th century.