Research at the Stanford University School of Medicine was the first ever to study a Neanderthal Y chromosome. Most investigations pertaining to our ancient relatives have aimed to show that modern human DNA is 2.5 to 4 percent Neanderthal DNA, from when modern humans and Neanderthals bred 50,000 years ago. The scientists discovered that the Neanderthal Y chromosome was not passed to humans at this period. Previously, most research from mitochondrial DNA indicates that Neanderthals and modern humans diverged anywhere from 400,000 to 800,000 years ago, but based on the Y chromosome in this study, scientists have been able to get a more specific estimate, which is around 550,000 years ago.
The team who worked on this study is not sure yet as to why there is no traces of the Neanderthal Y chromosome left in the human genome. Some theories are that the genes could have just drifted out of the gene pool by chance or that there Y chromosome is incompatible with homo sapiens genes.
I think that this particular study can be very beneficial for us to find out our ancestor's relationship with Neanderthals and how we lived, communicated, and bred with each other. Maybe it can also shed light on the how's and why's Neanderthals came to be extinct.