DNA from extinct species of hominids has always been found in the modern human genome, inherited from our ancient human ancestors. However, these pieces of ancient DNA have always been found in small sections, focusing on single-nucleotide substitution reactions and short sequences surrounding those. Now, long strands of neanderthal DNA have been found in the genomes of humans from Melanesia.
Almost all humans who's primary ancestry comes from outside Africa carry neanderthal DNA- those from south-east Asia may also have DNA from a group of ancient humans known as denisovans. Populations in Melanesia have been identified as having the highest percentage of long strands of ancient DNA from these ancient humans, with neanderthal DNA on chromosome 8 and denisovan DNA on chromosome 16.
These strands are the result of deletion and addition reactions, which obviously have a much larger effect on the genome than substitution reactions. They are also focusing on duplication mutations, which actually allows the original sequence to be maintained in it's original form.
While it would seem these genes have been selected by evolution overtime, it is still unknown what many of them actually do. This is hard to study as they are human specific genes, so there can be no accurate animal tests run on them. Additionally, due to the amount of mutations that have occurred in them overtime, its hard to get an accurate idea of what they were like in their original form.
Related Link (Effects of Neanderthal DNA in Humans): https://www.the-scientist.com/daily-news/effects-of-neanderthal-dna-on-modern-humans-30787