An exhibit displaying what neanderthals are supposed to have looked like. Source
A geneticist from Harvard has claimed that we could theoretically clone a neanderthal. The pre-human race has been dead for 30,000 years, but we reportedly have enough genetic information about them to eventually clone them. Many experts say that this will never happen, however, not because we don't have the technology to do it, but because the ethical concerns are too great. There would likely be many still births or horrible mutations in the early stages of testing, and there are other ethical and moral implications to bringing a human-like life into the world for the purpose of research. I think it would be really cool to bring an extinct race back to life, but I do agree that the ethical concerns are crippling.
ABC news has an article that is very informative, I suggest reading it.