Facts

We can study Neanderthal and modern human DNA to see if they interbred with modern humans.
We can study the DNA of Neanderthals because we have a large enough Neanderthal sample size (number of individual Neanderthals) to compare to humans.
Neanderthals are genetically distinct from modern humans, but are more closely related to us than chimpanzees are.
The Neanderthal and modern human lineages diverged about 550,000 years ago
So far, we have no evidence of Neanderthal mtDNA lineages in modern humans.
Neanderthals were not as genetically diverse as modern humans were at the same period, indicating that Neanderthals had a smaller population size.
Neanderthal nuclear DNA shows further evidence of small population sizes, including genetic evidence of incest.
As technology improves, researchers are able to detect and analyze older and more fragmentary samples of DNA.
Neanderthals have contributed between 1-4% of the DNA of humans of Eurasian descent.
Neanderthals have not contributed to the genome of African modern human populations because they never lived there and could not have interbred with the ancestors of those populations.
While we don't have evidence of Neanderthal mtDNA in the modern human gene pool, there are several possible explanations for this.