The conventional knowledge is that there were a series of migrations from Siberia over a land bridge near the end of the last ice age.
There are various anomalies which offer alternatives to the conventional knowledge, and unconventional, unrelated diffusionist theories abound, but no opposing theory has been definitively established.
In the United States physical anthropology (archeological investigations based on the study of human remains) is complicated by the Native American Graves Protection and Repatriation Act, (NAGPRA) which provides for the bodies of Native Americans and grave goods to be turned over to their tribe. In some cases, notably, that of Kennewick Man, this has affected human remains many thousands of years old which seem to have no connection to the modern tribes which are requesting relief under the act.
Further Reading