A team of German, American, Croatian and Finnish researchers have been studying remains of 38,000 year old Neanderthal for two years. The bone was found in a Croatian cave.
The evidence is from using mitochondrial DNA (mtDNA), which allows scientists to look much further at the ancestry background than nuclear DNA because it goes practically unchanged generation through generation by the mother. Nuclear DNA is a variation of several sets of DNA, and is what makes each of us individual from the other.
Well, evidence has been surmounting for years that Neanderthals split from anatomically modern humans later than believed, and with increasing advances in using mtDNA this has been easier to prove.
It is still clear that Neanderthals and modern humans could not breed, even during their temporal period of the 10,000-20,000 years that they lived contemporaneously to each other in Europe and parts of Western Asia. If they did breed (which there is evidence of some Neanderthal characteristics mixed with anatomically modern characteristics in other research being done) they could not produce fertile offspring, such as a horse and donkey producing a mule.
It is also still clear that Neanderthals became extinct about 30,000 years ago, which many believe was only due to the sweeping tribes of Homo sapiens. In fact, there is evidence of warfare between the two species, and remains of Neanderthals have been found in living sites of modern humans, often amongst rabbit bone and other midden, suggesting moderns ate them for supper.
Their interaction with anatomically modern humans did not stop at warfare, however, they even traded technology. For example, a Neanderthal tool, the Mousterian tool made "arrowheads" by using soft material, such as bone and antler, whereas years later, not too long before the disappearance of the robust species, moderns came up up with the Chatelperronian tool technique using hard substances, such as stone hammers.
The most mystifying evidence with Neanderthals, however, is their cranial capacity. Anatomically modern humans averaged, at the time of Neanderthals, around 1,100 to 1,200 cm³ while the very robust species' average brain size grew around 1,500 to 1,700 cm³.
The species is suggested by some researchers to have red hair on top of their naturally hairy bodies. The species was somewhat shorter than moderns averaging 5 feet 5 inches for males and 5 feet 1 inch for females. They also had rather large noses and generally robust features selected for cold weather, which can be seen in the picture (from Valley Anatomical Preparations, Inc.).
Some researchers argue that the two species could breed and produce fertile offspring, however, there is not enough Neanderthal genes present in the mtDNA of humans today to theorize that this is true. 
