Well this is turning into a bit of a Freak Week what with naughty fakirs and magnetic men so why stop now?
In the previous entry I mentioned I had very minor regurgitating skills but the real king of this is Stevie Starr. I saw him first do his tricks decades ago when he did his goldfish and Rubik cube trick which was pretty impressive but his act has developed over the years. You can see him at work here (as it is so difficult to describe):
A couple of videos of him on American talk shows (including Letterman and Leno, the former from 1988) running through the classics:
A long live video (pretty wild stuff and impressive too as he can keep things rolling for three quarters of an hour):
So how does he do it?
Well for starters it is perfectly possible to swallow things and bring them up on command. Starr has clearly had a lot of practice but from my more simple experiments (with a wadded up ball of bread) it is possible to swallow something, hold it in the top oesophagus (presumably just beyond the larynx) and then bring it back again. There are two stages to a swallow there is first the motion to the back of the throat and then there is the introduction to the alimentary canal. Pretty much once it gets far into stage 2 it is the straight run to the stomach and while it is possible to bring things back from there it is only with a lot of stomach contents too and throwing up on stage is not the desired effect (unless you are at a specialist establishment but that may be a story for another day). Instead you can store things quite happily somewhere at the base of the throat, talking naturally before coughing it back up again.
That said, a bit like Derren Brown, while there are real tricks going on as advertised, there also seems to be other fairly basic magic trickery at play to make some of the stunts look more impressive. Now I don't think he has anything as complicated as surgically implanted pockets of skin, as seen in the CSI episode "Abra Cadaver" (although the do usually use real-life cases and facts as the springboard to stories so they may be used by some for small items like lockpicks, although note at the end of the episode Grissom checks for these pockets in the suspect before the police cart him off and he then regurgitates the item in the closing shot), but I'd imagine parts of his stage act (his odd mannerisms for starters) are misdirection for some sleight of hand (especially the one where he swallows coins and brings them back up in order) and some of the stunts probably require some prep work and doubles of things made (worryingly I suspect he swallows the first Rubik's cube whole).
The Museum of Hoaxes has taken a look at him but really can't come up with more than "how does he do it??" although the comments contain more ideas including someone pointing to esophageal pouches, although that seems to be something seen in older men. As some commentators point out such an act has been relatively common on sideshows with Human Ostriches and Human Marvels has a good piece on one of the best known: The Great Waldo. There is also mention of a video from japan with him being X-rayed doing the trick where he swallows a locked padlock and a key and unlocks it and I'll keep an eye out for that.
Most interesting they do give examples of historical vomiters, although one does wonder if some of them are suffering from pica (I'll do more digging):
Incidentally, history is full of famous vomiters, so Stevie Starr evidently isn't the only one who has ever had this talent. In 1621 there was the case of the nail-vomiting Boy of Bilston (who had been trained by a priest to simulate the symptoms of being bewitched). This was followed in 1642 by Catharina Geisslerin, "the toad-vomiting woman of Germany," who, as you might guess, had a talent for vomiting up toads. In 1694 there was Theodorus Döderlein, who vomited up twenty-one newts and four frogs.
Damn Interesting also has a look at this class of entertainer in particular the Great Regurgitator who worked in the early 20th Century. The climax to his act was drinking a gallon of water and a pint of kerosene. He would first spit out the latter lighting it so as to st fire to a little metal castle before putting the fire out by squirting the water all over it. This "water spouter" act seems to have been around since the 17th Century but he and Harry Morton "The Human Hydrant" were the last of their type, mainly because the whole thing was pretty vile. Other performers did "dry" regurgitating in the middle of the 20th Century but it seems that Stevie Starr is one of the last performers in this niche. I am unsure if this is a good or a bad thing.
NB: As you are dicking around with things close to your lungs it is possibly not wise to experiment with this in case you end up choking to death. Also it might not work for everyone - it may be unconnected but I do have a hyperactive gag reflex (endoscopes are Hell) which might be part of the technique. Also, of course, he might be doing something completely different - still doesn't mean you can run of experimenting 