Anyone who hasn't read this article yet should do so immediately:
It's an older story (2013), but this particular site just posted it now which prompted me to relay it to you.
It's well-written, a fun story to read, and has some amazing insights into what the future may hold for regeneration. The researcher, named Michael Levin, has been studying how electrical signals can be used to tell the body to start regenerating limbs and organs. So far he has only been able to get it to work on frogs, but the article states that his next project, which he is supposedly working on last year to current, is testing mammals - starting with mice. The initial test they are conducting is attempting to regenerate a mouse's digits completely after they have been cut off.