There are various theories about how indigenous people arrived in the Americas. The most widely accepted theory in archaeology is called the Land Bridge Theory. This theory suggests that Native Americans arrived in the Americas during the last ice age, before 10,000 years ago. Migrants fanned out across the continent chasing large game through ice free corridors. Recent genetic studies suggest that this happened in waves and not all at one time.
The most widely accepted theory about the Caribbean is that the original inhabitants were of Amazonian origin. Indigenous people made their way up the Amazon River to the coast and settled. Over time, they made their way to the various Caribbean Islands. Genetic studies have suggested a significant Native American ancestry in present day Puerto Rico which supports the theory of migrations from the Amazon River.
The origins of indigenous people in the Americas is a study that is exciting in the field of archaeology. New technologies like the study of DNA promise to enlighten us further about events that happened over 10,000 years ago.