For one thing, they had to cope with injuries inflicted by large wild animals they were hunting:
Researchers investigated the skeletal remains of more than 30 individuals where minor and serious injuries were evident, but did not lead to loss of life. The samples displayed several episodes of injury and recovery, suggesting that Neanderthals must have had a well-developed system of care in order to survive.
…
“We have evidence of healthcare dating back 1.6 million years ago, but we think it probably goes further back than this. We wanted to investigate whether healthcare in Neanderthals was more than a cultural practice; was it something they just did or was it more fundamental to their strategies for survival?
“The high level of injury and recovery from serious conditions, such as a broken leg, suggests that others must have collaborated in their care and helped not only to ease pain, but to fight for their survival in such a way that they could regain health and actively participate in the group again.” Samantha Martin, “Neanderthal healthcare practices crucial to survival” at Phys.org
These must have been different Neanderthals from the brutes we learned about years ago.
Unfortunately, the story at Phys.org is marred by “evolution-speak.” What on earth does it mean to wonder “whether healthcare in Neanderthals was more than a cultural practice; was it something they just did or was it more fundamental to their strategies for survival?” How could it fail to be both?
Underlying such helpless mulling is the problem that in any Darwinian scheme, someone must be the subhuman. Thus, ordinary and obvious human behavior cannot be allowed to sound ordinary and obvious. The search is on for a time when people set broken legs for no particular reason that they understood. It just happened somehow because it spread their selfish genes.
See also: Neanderthals had a sophisticated home life?
and
Neanderthals did know how to start fires