If you have a hard time following all the Neandertal genomics findings from the last few years, and their implications, National Geographic has a really thorough piece up. It’s a good digest of all the news you can use. One thing I would like to add: from what I can tell the probability of the signals of admixture in non-Africans being genuinely Neandertal seem to be increasing as we progress. In other words, you should weight the “other side” (ancient population structure, where some African populations were closer to Neandertals before they left Africa) less than you did in 2010.
Of course one of the more inevitable aspects of the admixture story has been the humanization of Neandertals. I don’t know how I feel about this. Should our own affinity to Neandertals alter our view of their behavior or anatomy? Plenty of behaviorally anatomically modern humans were beastly after all.