I’m not sure they’re even to the point of being able to reattach the nerves in, say, a severed finger. I think they can do the mechanical stuff but not the “wiring”.
I don’t know how the nerve endings work but there was a blues man who had his finger tip reattached with just a wrapping of balm and spider webbing.
http://www.chron.com/entertainment/music/article/Earl-Gilliam-sings-lives-the-blues-1725886.php
He holds up his “trigger finger,” a long, brown, spidery digit that has pounded out blues songs on a keyboard for the better part of seven decades. The tip of the finger is positioned at a permanent right angle, the result of a lawn mower accident when he was a kid. “My mother didn’t believe in doctors,” he says. So she reattached the fingertip, splinted it using spider webs as a wrap and soaked it in vinegar. “That’s just the way it healed,” he says, smiling. “Told you, she didn’t believe in doctors.”