Now that the human genome has been sequenced, and Neanderthal genes have been found in up to 4% of our DNA, we can no longer deny our ancestral roots. Some of us have more of it and others less. Asians and the native people of Oceana have more Denisovan genes than the Neanderthal genes, up to 5% in some of them. Denisovans were not a known hominid species until recently when a discovery in Siberia of hominid skeletal and dental remains was uncovered. The DNA was neither Homo sapiens or Homo neanderthalensis but a heretofore unknown hominid.
Neanderthal (also written as Neandertal) appeared in the Pleistocene Epoch (2.6 million years to 11,800 years ago) first found in the Neander Valley (Tal) in Germany. When first discovered in 1856, they were thought to be deformed H. sapiens, but when they were found all over Europe and the Middle East, the deformed theory was discarded and they got their own species name, even though some paleontologists thought that a bit premature. Strangely, 25,000 years ago Neanderthals disappeared. Charles Darwin published The Origin of Species in 1859. Various theories of their extinction have been postulated. This was in the midst of the last ice age. Could that have been their death nail? Did we out-hunt them, competing for every bit of protein in the cold barren land that was overwhelmed with ice? Did we absorb them as suggested by our own DNA? Or did we kill them? There is evidence of cannibalism that could have contributed.
Getting back on how to recognize them within and amongst us. They actually had a larger brain housed in a lower profile cranium. The brows were more prominent, and the nose and eye sockets had bigger openings. The front teeth were larger, spaced farther apart, and the occipital ridges were more prominent, suggesting stronger posterior neck muscles.
The chin was what we would classify as weak. Their hyoid bone in front of where the voice box would be, suggested they had similar linguistic skills to 
us. Also, they could not have had the stone tool technology and social customs, such as the burial of the dead, decorative arts, and even flute-like musical instruments without language. They had pale skin and possibly red hair, making them more sensitive to UV light and prone to skin cancers. Other genetic studies suggest they were prone to depression and eating disorders.
They did not have the ability to domesticate animals and lacked dogs that could have helped them in hunting larger game. This lack of skills with taming animals may have contributed to their demise.
Putting it all together. If you see a red-haired very muscular person, especially the back of the neck, about 5 foot 5 inches tall, a barrel chest with large hands and size 13 shoes, a weak chin, prominent brows and premature aging from sun damage, with possibly a skin lesion or two, who is kind of mean, hates dogs, and is grouchy, you may be meeting one of them.