Columbus' original mission was to find a passage across the Atlantic to establish trade routes with the Far East. When Columbus arrived in the Carribean, he thought he was in the East Indies (hence the use of the term "Indians" for the indiginous people of the Americas). Later Spanish missions would attempt to establish colonies and spread Christianity.

Columbus' expeditions were funded by the Spanish king and queen, Ferdinand and Isabella.

Caravels were invented in Portugal in the fifteenth century. They were extremely maneuverable and allowed Portugal to explore the African coast and the Indian ocean at remarkable speeds.

Hernan Cortes and Francisco Pizarro were both Spanish Conquistadors who arrived in South America in the sixteenth century. Using similar tactics that relied on superior weaponry and manipulating old tribal rivalries, Cortes and Pizarro were able to tear down the two largest civilizations—the Aztecs (Cortes) and the Inca (Pizarro)—in what is now called Latin America.

The early Spanish explorers and colonizers were insatiable in their quest for gold and silver. Driven by the promise of rich reward, they sacrificed the lives of hundreds of thousands of Native Americans and mined deep into the heart of the South American continent. In one way, they were succesful—the amount of gold and silver they flooded into the European market was unprecedented; however, in the long term, the result was almost as bad for Spain as it was for South America. The Spanish companies and individuals owed so much debt to British and Dutch investment banks and companies that the profit ended up in the hands of others and the price of gold and silver in Spain plummeted.

All of these individuals were involved with Portugese exploration except for Christopher Columbus, who was actually born in Italy but sailed to the New World under the patronage of the Spanish monarchs Ferdinand and Isabella.

Captain James Cook is most famous for a series of explorations of the Southern Pacific Ocean. He was the first European to lead an expedition to mainland Australia; the first European to circumnavigate New Zealand; and the first European to land in Hawaii. He achieved this in the eighteenth century.

Ferdinand Magellan led the first expedition to successfully circumnavigate the globe from 1519 to 1522. Rather unfortunately for Magellan, he died near the end of the journey, so he is not actually the "first man to circumnavigate the world". However, he is remembered as such as he was the leader of the expedition.

Vasco da Gama was a Portuguese explorer in the late fifteenth and early sixteenth centuries. He is most famous for being the first European to sail to India. He is thus credited with opening up trade between Europe and the Far East via the ocean, a trend that would propel the Portuguese, Dutch, Spanish, French, and English to global prominence.

Henry Hudson was employed by the Dutch East India Company to find the fabled Northwest Passage to Asia through the continent of North America. He sailed up the Hudson River (named after him) and found a passage into the heart of modern Canada, but could not proceed further because his crew mutinied. The Northwest Passage, was finally successfully completed in 1906 by Norwegian explorer Roald Amundsen.