Here's another example of how genetic methods can shed light on archaeological questions, Paleo-Eskimo mtDNA Genome Reveals Matrilineal Discontinuity in Greenland:
The Paleo-Eskimo Saqqaq and Independence I cultures, documented from archaeological remains in Northern Canada and Greenland, represent the earliest human expansion into the New World's northern extremes. However, their origin and genetic relationship to later cultures is unknown. We sequenced a mitochondrial genome from a Paleo-Eskimo human, using 3400- to 4500-year-old frozen hair excavated from an early Greenlandic Saqqaq settlement. The sample is distinct from modern Native Americans and Neo-Eskimos, falling within haplogroup D2a1, a group previously observed among modern Aleuts and Siberian Sireniki Yuit. This suggests that the earliest migrants into the New World's northern extremes derived from populations in the Bering Sea area, and were neither directly related to Native Americans nor the later Neo-Eskimos that replaced them.
New Scientist has a popular press profile of the research & findings. Remember last year when it was confirmed that Polynesians had to have been visiting the coast of South America because of the phylogeny of chicken DNA extracted from subfossils? Though there have always been hints, I think this suggests greater complexities to our picture of the pre-Columbian world. Do note that this is one mitochondrial DNA lineage. It shows lack of perfect continuity, but does not entail total replacement....
Update: "Polynesian" chickens might not be in the bag yet. See comment.
"The previously published, apparently pre-Columbian, Chilean specimen and seven pre-European Polynesian specimens, also cluster with the same European/Indian subcontinental/Southeast Asian sequences, providing, at this stage, no support for a Polynesian introduction of chickens to South America."
Greenberg's linguistic theory has three waves of migration via the Bering Strait: Amerinds, Na-Dene (Athabaskans / Navaho), and Eskimo / Aleuts. The new theory just groups the Paleo-Eskimos with Aleuts rather than with Eskimos. It's a rather small change.
The Dorset culture (called Tuniit by the Inuit) preceded the Eskimos (Thule culture) in arctic America. They were gradually replaced after 1000 CE by the real Inuits. The seem to have been already in decline when the new immigrants arrived in any case.
I don't think this particular case is any mystery in itself (Inuits are a recent arrival, we alredy knew it), though the aDNA found may help explaining the origins of the Dorset people anyhow.
The Inuit reached Greenland about the same time the Norse did. The Norse had contact with some native group, but I don't know whether it was Inuit or some Native American tribe.
Out of curiosity, exactly how are people separating Inuit from Laplander in all this. Are the Inuit coming over from Siberia whereas the Laps are coming from the other direction?
The Laplanders (Sami) are by modern research (DNA) probably the oldest Europeans and even less closely related to Siberian and/or Mongol populations than other European populations.
The connection between Finns and Laplanders is even more complicated, though both speak Finno-Ugrian language. Finno-Ugrian language might have some slight connections (words) also with Chukhian language close Bering.