The study of Neanderthal cognition is difficult, because of the archaeological invisibility of cognition, and because of the methodological issues that arise both from that invisibility and from their being close to modern humans. Nevertheless, fair progress has been made in gathering relevant evidence. There is now good evidence that Neanderthals were cognitively sophisticated, displaying many of the cognitive traits that were traditionally regarded as proxies for modern human cognition, notably including language. It can neither be proven nor excluded that they were our cognitive equals, but they were close enough to us, biologically and cognitively, to interbreed successfully and leave a genetic legacy in our DNA.