It's one of The Doctor's most amazing feats, the ability to cheat death by changing his form and adopting a new face and personality. How exactly the process works remains a mystery explored in depth only in non-television media, and therefore is of dubious canonicity. Still, there's a fair amount of little-known trivia about regeneration.
10. It Was Initially Extremely Stupid How to get the aging, ill and expensive William Hartnell out of the role of The Doctor and replace him with a new actor didn't jump fully formed from a writer's brain. The first suggestion was to just literally switch him out during "The Celestial Toymaker" and play it off like magic. When the BBC scrapped the idea the more biological explanation was written in. However, the effect was going to be accomplished simply by having Hartnell fall down with his cape over his face, only for it to be revealed as Patrick Troughton underneath in the next shot. Luckily, a vision mixer named Shirley Coward came up with a more impressive sequence, and long history of effects-laden regenerations has been the norm since then.
9. It Was Supposed to be Horrifying for The Doctor In a production note from 1966 the process (called then simply a "metaphysical change") was the equivalent to having a LSD flashback. The Doctor would relive all of the most horrible and painful memories of his life while it took place, including the alleged war on their home planet that was presumed to be the reason The Doctor and Susan fled. This concept was explored later when the Fifth Doctor regenerated.
8. It Was Years Before Even the Producers Knew What it Was Despite using the trick to transform Hartnell into Troughton it wasn't until 1974 that regeneration got a name and was established in the canon definitively. The Second Doctor simply remarked that he had been renewed, and when he regenerated into the Third the Time Lords merely remarked that his appearance was to change as part of his punishment of exile on Earth. When Jon Pertwee ceded the role to Tom Baker, regeneration was finally named.
7. Time Lords Can Change Genders (For a Terrible Reason) It's been firmly established now in the television canon that Time Lords are capable of swapping sexes through regeneration. The Eleventh Doctor mentioned his friend The Corsair doing so, and Missy appeared as a female Master last season (admittedly we don't know if that was actually caused by a regeneration... trying to make sense of what proper incarnation of The Master we're currently on would give anybody a headache). The concept was also explored in the 2003 Big Finish audio story "Exile", where the Second Doctor is played by Arabella Weir. According to the story, Time Lords swap sexes if they regenerate as a result of a suicide. How literally this should be taken is open to interpretation, as arguably the Tenth Doctor committed suicide to save a companion. Interestingly enough, the Eleventh Doctor believes at first that he is a girl.
6. Its Design Was Initially Really Classist and Racist The strongest history of regeneration in narrative comes from the audio play "Zagreus", which was made canon along with the rest of the Eighth Doctor's post-1996 adventures in "The Night of The Doctor". In "Zagreus" Rassilon developed regeneration to simulate the immortality of the ancient Gallifreyan enemies the Great Vampires. Once achieved, he planned to use his newfound power to woo the Gallifreyan elite, who were to be the only ones allowed to undergo the process. From there he embarked on a racially motivated plan of genocide designed to eliminate all non-humanoid sentient life in the universe. Somehow you'd think something as monumental as regeneration would not be used as the gateway to being the biggest jerk in the universe.
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5. It Actually is Possible to Regenerate Into Previous Forms It was a great moment for fans when Tom Baker appeared in "The Day of The Doctor" as the Curator a (possibly) future incarnation of The Doctor that once again dons the face of the beloved Fourth Doctor. The concept was first explored in the 1994 novel State of Change. In it the Sixth Doctor claims that very skilled Time Lords could retro-regenerate, though he also says it is extremely difficult and rare to the point he isn't sure he had ever really seen it. In that same book, he is able to summon the mind of the Third Doctor and his skill with hand-to-hand combat. So buck up avid Tennant fans, it actually is remotely possible he will one day be The Doctor again.
4. It Briefly Creates Two Minds in One Body The regeneration process is not instantaneous. For at least some part of it both the dying Doctor and the coming Doctor exist simultaneously as one entity. This is best seen in The Watcher, a partial version of The Doctor who helps guide the events of "Logopolis" before merging with the Fourth Doctor to become the Fifth. The short story "The Touch of the Nurazh" also explored the idea when the Third Doctor suffered a fatal fall and the titular Nurazh attempted to possess his body as it entered his regeneration cycle. The combined power of the Third and Fourth Doctors working as one was enough to expel the Nurazh and halt the death of the Third Doctor.
3. It's Unclear What Happens When There Are No More Regenerations The question of what happens when there are no more regenerations was tabled in "The Time of The Doctor" when the Time Lords granted The Doctor a new lease on life with unknown limitations. There have been several different conflicting ideas about what happens when those regenerations run out. In "Mawdryn Undead" it's heavily implied that Time Lords who run out are simply no longer Time Lords, while a Seventh Doctor comment states that a Time Lord out of regenerations breaks down into molecules. We do know from "The Twin Dilemma" that actively attempting to regenerate with no more left is fatal.
2. What Can Stop Regeneration? The process is not infallible. Certain types of injuries can subvert regeneration. Some of these are well known such as destroying both hearts of a Time Lord while they are in the middle of regenerating. Lesser known causes include extreme blood loss and several substances like diazepam and propofol, anesthetics used in open heart surgeries. Both the Time Lords and the Daleks developed specialized weaponry to stop regenerations.
1.It's Real Not in humans, alas, although we actually have figured out the two heart thing. It turns out that flatworms have the ability to not only live forever, but also that you can get them to basically regenerate their whole bodies at a cellular level including their brains. For all intents and purposes the process is the same as the one The Doctor undergoes, though how we can adapt this discovery to humans is still unknown. Really at this point it's a race to see whether we figure it out before flatworms invent TARDISes.
Doctor Who returns later this year with "The Magician's Apprentice".