Scienece grows and develops based on evidence; Darwin looked at finch bills on an isolated island and inferred that they came from the same ancestors and had specialised over time for particular ecological niches. He was right. You can run genetic profiles to prove it.
People found fossils of hominds like the Neanderthals, and inferred they were ancestors. They then found that H. sapiens and Neanderthals had co-existed, and speculated they had interbred. Now they've got a good enough genetic window, they've found that while related, H. sapiens did not descend from Neanderthals.
Neanderthals were very like us; some people could probably pass for Neanderthals, and some Neanderthals for H. sapiens.
Neanderthals also had some concepts that lead them to show what we would call respect for the dead. There's been some speculation that Neanderthals didn't have 'art'; here's a good article;
http://www.sciencemag.org/cgi/content/full/282/5393/1451
Others have speculated that runaway sexual selection lead to creative intelligence in H. sapiens mushrooming, and that this process didn't occur in Neanderthals. The Mating Mind by Dennis Miller examines this.