Neanderthal genetics

Genetic studies on Neanderthal ancient DNA became possible in the late 1990s.
The Neanderthal genome project, established in 2006, presented the first fully sequenced Neanderthal genome in 2013.
Since 2005, evidence for substantial admixture of Neanderthals DNA in modern populations has accumulated.
The divergence time between the Neanderthal and modern human lineages is estimated at between 750,000 and 400,000 years ago.
The more recent time depth has been suggested by Endicott et al. (2010)
and Rieux et al. (2014)
A significantly deeper time of separation, combined with repeated early admixture events, was calculated by Rogers et al. (2017).
On July 3, 2020, a team reported finding that a major genetic risk factor of the Covid-19 virus was inherited from archaic Neanderthals 60,000 years ago. This risk is conferred by a genomic segment inherited from Neandertals and occurs at a frequency of ~30% in south Asia and ~8% in Europe.
Genome sequencing.
In July 2006, the Max Planck Institute for Evolutionary Anthropology and 454 Life Sciences announced that they would sequence the Neanderthal genome over the next two years. It was hoped the comparison would expand understanding of Neanderthals, as well as the evolution of humans and human brains.
In 2008 Richard E. Green et al. from Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany, published the full sequence of Neanderthal mitochondrial DNA (mtDNA) and suggested "Neanderthals had a long-term effective population size smaller than that of modern humans."
In the same publication, it was disclosed by Svante Pääbo that in the previous work at the Max Planck Institute, "Contamination was indeed an issue," and they eventually realised that 11% of their sample was modern human DNA. Since then, more of the preparation work has been done in clean areas and 4-base pair 'tags' have been added to the DNA as soon as it is extracted so the Neanderthal DNA can be identified.
The project first sequenced the entire genome of a Neanderthal in 2013 by extracting it from the phalanx bone of a 50,000-year-old Siberian Neanderthal.
Among the genes shown to differ between present-day humans and Neanderthals were "RPTN", "SPAG17", "CAN15", "TTF1", and "PCD16".
A visualisation map of the reference modern-human containing the genome regions with high degree of similarity or with novelty according to a Neanderthal of 50 ka has been built by Pratas et al.
Interbreeding with anatomically modern humans.
Researchers addressed the question of possible interbreeding between Neanderthals and anatomically modern humans (AMH) from the early archaeogenetic studies of the 1990s. 
In 2006, no evidence for interbreeding had yet been found. 
In 2009, analysis of about one third of the full genome of the Altai individual was still reported as showing "no sign of admixture". The variant of microcephalin common outside Africa, which was suggested to be of Neanderthal origin and responsible for rapid brain growth in humans, was not found in Neanderthals. Nor was a very old MAPT variant which is found primarily in Europeans.
Positive evidence for admixture was first published in May 2010. Neanderthal-inherited genetic material is found in all non-African populations and was initially reported to comprise 1 to 4 percent of the genome. This fraction was later refined to 1.5 to 2.1 percent.
It is estimated that 20 percent of Neanderthal DNA currently survives in modern humans.
Modern human genes involved in making keratin, a protein constituent of skin, hair, and nails, have especially high levels of introgression.
For example, the genes of approximately 66% of East Asians contain a POUF23L variant introgressed from Neanderthals, while 70% of Europeans possess an introgressed allele of BNC2. 
Neanderthal variants affect the risk of developing several diseases, including lupus, biliary cirrhosis, Crohn's disease, type 2 diabetes, and severe COVID-19. The allele of MC1R which was originally linked to red hair in Neanderthals is not found in Europeans, but is present in Taiwanese Aborigines at a frequency of 70% and at moderately high frequencies in other East Asian populations; hence, there is actually no evidence that Neanderthals had red hair. 
While interbreeding is viewed as the most parsimonious interpretation of these genetic findings, the 2010 study still could not conclusively rule out an alternative scenario, in which the source population of non-African modern humans was already more closely related to Neanderthals than other Africans were, because of ancient genetic divisions within Africa.
Research since 2010 has refined the picture of interbreeding between Neanderthals, Denisovans and anatomically modern humans.
Interbreeding appears to have occurred asymmetrically among the ancestors of modern-day humans, and this may explain differing frequencies of Neanderthal-specific DNA in the genomes of modern humans. Vernot and Akey (2015) concluded that the relatively greater quantity of Neanderthal-specific DNA in the genomes of individuals of East Asian descent (as compared with those of European descent) cannot be explained by differences in selection. 
They further suggest that "two additional demographic models, involving either a second pulse of Neandertal gene flow into the ancestors of East Asians or a dilution of Neanderthal lineages in Europeans by admixture with an unknown ancestral population" are parsimonious with their data. 
Kim and Lohmueller (2015) reached similar conclusions: "It has been hypothesized that the greater proportion of Neandertal ancestry in East Asians than in Europeans is due to the fact that purifying selection is less effective at removing weakly deleterious Neandertal alleles from East Asian populations. Using simulations of a broad range of models of selection and demography, we have shown that this hypothesis cannot account for the higher proportion of Neandertal ancestry in East Asians than in Europeans. Instead, more complex demographic scenarios, most likely involving multiple pulses of Neandertal admixture, are required to explain the data."
Khrameeva et al. (2014), a German-Russian-Chinese collaboration, 
compiled a consensus Neanderthal genome based on the genome of the Altai individual and of three Vindjia individuals. 
This was compared to a consensus chimpanzee genome as the outgroup
and to the genome of eleven modern populations (three African, three East Asian, three European). 
Beyond confirming the significantly higher similarity to the Neanderthal genome in non-Africans than in Africans, the study also found
a difference in the distribution of Neanderthal-derived sites between Europeans and East Asians, suggesting recent evolutionary pressures. Asian populations showed clustering in 
functional groups related to immune and haematopoietic pathways,
while Europeans showed clustering in functional groups related to the lipid catabolic process.
Kuhlwilm et al. (2016) presented evidence for AMH admixture "to" Neanderthals at roughly 100,000 years ago.
There have been at least three episodes of interbreeding. The first would have occurred soon after some modern humans left Africa. The second would have occurred after the ancestral Melanesians had branched off—these people seem to have thereafter bred with Denisovans. The third would have involved Neanderthals and the ancestors of East Asians only.
A 2016 study presented evidence that Neanderthal males might not have had viable male offspring with AMH females.
This could explain why no modern man to date has been found with a Neanderthal Y chromosome.
A 2018 study concluded that interbreeding between Neanderthals and modern humans led initially to the exposure of each species to unfamiliar viruses. Later on, the exchange of genes granted resistance to those viruses, too. 
On July 3, 2020, scientists reported finding that a major genetic risk factor of the Covid-19 virus was inherited from archaic Neanderthals 60,000 years ago. It is estimated that 16% of people in Europe and 50% of people in south Asia have the particular sequence on chromosome III,
with 63% of Bangladeshis having these gene sequences. Africans, Middle Easterners and East Asians feature the presence of the chromosome in very negligible amounts.
Epigenetics.
Complete DNA methylation maps for Neanderthal and Denisovan individuals were reconstructed in 2014. 
Differential activity of HOX cluster genes lie behind many of the anatomical differences between Neanderthals and modern humans, especially in regards to limb morphology. In general, Neanderthals possessed shorter limbs with curved bones.