Despite very extensive research using the fossil record and remains of artefacts, it's still unknown whether the Neanderthal people :
Many other aspects of their culture are completely unknown - see Wikipedia link above.
Also see : Neanderthal extinctionplugin-autotooltip__plain plugin-autotooltip_bigNeanderthal extinction
In August 2014 an international research team reported (in Nature 512, pages 306–309 [ paywalled ] ) on a new analysis of 40 sites in Western Europe - concluding that Neanderthals died out about 40,000 years ago.
There are numerous theories which attempt an explanation of their extinction - including :