In the 15th century the New World was called simply Western Indies by the Spaniards who claimed the first right to name it in virtue of the discoveries of Columbus. In the following century Martin Waldseemuller, a German cosmographer, unaware of previous discovery, proposed the name America in honor of Amerigo Vespucci who claimed to have touched the western continent on his first voyage, 1497-98. Of the many claims to pre-Columbian discovery (Phoenicians, Basques, Celts, Norse, Italians, and Chinese), the Norse alone is accepted as historically certain. However, Ari Thorgilsson (died 1148), most trustworthy of the historians of Iceland, records evidence of occupation of Iceland by Irish monks before the arrival of the Norse, and reference is made to a land in the western ocean called Ireland the Great in the "Saga of Thorfinn Karlsefni," "Eyrbyggia Saga," and narratives of Are Marson. Adam of Bremen, in "A Description of the Northern Islands" (1075), mentions Greenland and Vinland and gives the oldest written account of Norse discovery of America. Greenland was settled by Eric the Red c.985,and the discovery of Vinland is ascribed to Leif, son of Eric, on his way back to Norway from Greenland where he had been sent by King Olaf of Norway to introduce Christianity (c.1000). The first diocese in the new world was erected at Gardar, Greenland, c.1125,and its existence is corroborated by several letters in the Vatican Library.

Columbus arrived at San Salvador (Watling Island) in 1492 and proceeded to Cuba and Haiti, discovered Jamaica in 1494, and in 1498 came to Trinidad and the mainland. Spanish exploration and conquest followed rapidly, and as Portuguese rivals disputed Spanish claims, an appeal was made by both governments to Pope Alexander VI, who in 1493 delimited two spheres of influence by a line drawn 370 leagues west of Cape Verde Islands, the western to be Spanish, the eastern Portuguese. Spain began colonization of the larger Antilles in 1493. Balboa established the continental nature of America by discovery of the Pacific in 1513. Cortes conquered Mexico in 1521, Central America was subjugated in 1524, and in 1534Peru was conquered by Pizarro. Within sixty years of discovery, all Central and South America, except Brazil, and a large part of North America belonged to Spain. Conversion of the Indians was stipulated in every royal contract with the explorers, and the Church undertook education and civilization of the Indians as soon as governmental administration was stabilized. The printing press was introduced into Mexico (c.1536) for this purpose, and Franciscans, Dominicans, and other religious orders, especially Jesuits, became the protectors as well as the teachers of the natives. The Brazilian coast was discovered by Pedro Alvarez Cabral in 1500, and the methods of Portuguese colonists, though more commercial, resembled those of Spain, but in the 17th and 18th centuries they became dangerous to Jesuit missions through their practise of enslaving the Indians.

The first French colony was established in 1534 at the mouth of the Saint Lawrence explored by Champlain, the first permanent settlement at Quebec in 1608, and French power in Canada was strengthened by the Jesuits, who strove to win the Iroquois to Christianity and friendship with France. Connection between the Great Lakes and the Mississippi was established in the 17th century by Marquette and Joliet. The French also colonized Louisiana, the Mississippi Valley explored by La Salle, some of the Lesser Antilles, and Guiana in South America, but their undertakings were on a smaller scale than the Spanish and less actively supported by the government.

The English flag was brought to America in 1491 by John Cabot, a Venetian navigator commissioned by King Henry VII, who landed near Cape Breton. In 1584,1601 settlements were made in North Carolina and Virginia under the patronage of the crown, and later by the Puritans in New England, and by Catholics in Maryland. The English were superior to the French in organization and displayed more individual enterprise and commercial tendency than the Spanish. Dutch and Swedish migrations followed, and in 1613 the colony of New Netherlands was founded, extending from Long Island up the Hudson River Valley. The colony of New Sweden, founded in 1638 on the shores of Delaware Bay, was ceded to the Dutch in 1655, and in 1664Dutch possessions passed to the English. Unfortunately those in authority did not always encourage the civilization of the Indians but too often regarded them as obstacles to be removed.