The early part of the story
20.03 The 20th miner to be pulled out of the mine is Dario Segovia. Just 13 to go.
19.28 Pablo Rojas has appeared! He's the 19th miner to be brought safely to the surface. He's greeted by the usual cheering and clapping. He looks in good shape and waves to the crowd. Only 14 to go.
19.23 On appearing at the surface every miner is taken to hospital for a thorough medical check. Officials have just said that every miner so far has been in a good condition.
19.11 The capsule is back underground to fetch Pablo Rojas, the 19th miner. That Phoenix 2 never stops. Mr Golborne, Chile's mining chief, has said it is unlikely that Phoenix 1 or 3 will be used... unless 2 gets a few scrapes. So far it is holding up well!
19.10 Jaime Urzua whose brother, Luis Urzua, 54, will be the last of the 33 miners to be rescued, has told BBC Mundo: "He has been with his colleagues all the time and helped them. He will accompany them to the end and it makes us proud because it will be for the good of all the miners."
19.07 Quote of the day so far? Perhaps this from Mario Sepulveda, the second miner to be pulled from the mine: "I have been with God and I've been with the devil. They fought but God won."
19.00 Pablo Rojas , the cousin of Esteban, will become the 19th miner to be rescued. He had worked for the mine company for just six months before it collapsed.
18.55 The operation will have to quicken the pace if, as Laurence Golborne, says it will finish by the end of today. Remember, Chile is four hours behind British Summer Time so it could all be over by 4am on Thursday. Everything has been meticulous so far, though, and the rescuers may be reluctant to change their strategy.
18.52 The rescues are becoming routine now. Let's hope it stays that way. 18 down, 15 to go.
18.49 Here he comes. The glare of the sun greets Esteban Rojas. The 44-year-old, father of three, becomes the 18th miner to be rescued. He is greeted by his girlfriend who said yes to his marriage proposal while underground.
18.41 Is Laurence Golborne, mining minister, the most popular man in Chile? Approval ratings of 86 per cent suggest he is. President Pinera is not far behind though.
18.31 The capsule has returned to the mining chamber. Esteban Rojas, the 18th miner set to be rescued, will see daylight soon.
18.25 Katty Kay of BBC World News America tweets that the mine rescue is a boon for President Pinera.
18.17 Chile's mining minister Laurence Golborne says ever miner could be rescued by the end of the day. A monumental effort if true. Original estimates put the operation at lasting 48 hours.
18.13 Small hiatus while technicians do checks on Pheonix 2 to make sure it is still in good order. There was a small problem with the door but it has now been fixed. Esteban Rojas will be up once the capsule is moving again.
18.08 Nasa which advised the rescue have praised the successful operation so far. Charles Bolden, the space agency's chief, said: "I am proud of the people of this agency who were able to bring the experience of spaceflight down to Earth when it was needed most.
"On behalf of the entire NASA family, I want to ask that our heartfelt thoughts and prayers continue to go out to the courageous miners, their families and friends, and the dedicated people who have been working to safely reach those who are still trapped underground."
17.50 The 18th person will be Esteban Rojas, 44, and who is in charge of maintenance in the mine. He has promised to marry his girlfriend of 25 years when he gets out of the mine. The world awaits.
17.48 Let's recap. 17 miners are now above ground with 16 below. We are past half-way!
17.45 Argentine President Cristina Fernandez, writing on twitter says: "I've just spoken to Sebastián Piñera. Huge emotion. I said to him "You look like Mario Sepúlveda?, the second rescued miner..."
"I watched it live. Sepúlveda rousing everyone from the tunnel. After, unstoppable. What strength, what "polenta" (trans: energy, liveliness, force), smiling, happy, optimistic."
"Chi, Chi, Chi, le, le, le, Viva Chile! And he gave stones as gifts that he brought up in his rucksack. He didn't throw them; he gave them to people euphorically and gratefully."
17.39 Omar Reygadas emerges from the mine becoming the 17th to be rescued
17.30 While we wait for Omar Reygadas let's revisit that song idea. Animals' We Gotta Get Out of This Place works. Or maybe The Only Way is Up. Can you think of better? Comment below if you can!
17.29 Local media in Chile is reporting that the miners and rescue workers underground are having a lunch of mashed potato and fish, finished off with pineapple for dessert. Sounds yummy.
17.21 Next up is Omar Reygadas. He'll be the 17th miner to appear, meaning that more than half will have been rescued. Woohoo!
17.18 Barack Obama is now getting in on the act. The US President's press secretary, Robert Gibbs, says Mr Obama thinks the rescue of Chilean miners is a "truly inspirational story with a very happy ending."
He plans to telephone Chilean President Sebastian Pinera, Mr Gibbs says. David Cameron spoke to Mr Pinera earlier today.
17.15 The wheel has stopped turning. Let's hope it's because it has reached the bottom of the mine and not because it is stuck!
17.12 So, some information about our next miner to appear. Omar Reygadas was a bulldozer operator at the mine. While trapped underneath the ground the 56-year-old asked for steak and television. Good man.
17.09 Back to that song theme. How about Men at Work - Down Under? Or Here Comes the Sun. That has to be the most appropriate!
17.08 It's announcd that Omar Reygadas will be the seventeenth man to be rescued
17.05 Ok, let's try to liven this thing up even more. What songs are appropriate to greet the miners on the surface? M People's Moving On Up? Ray of Light by Madonna? Cigarettes and Alcohol by Oasis.
16.56 The Phoenix capsule is starting to look slightly dusty and battered but it is being checked regularly between descents
16.54 Right, now we wait for miner number 17 but who is it going to be?
16.52 He thanks the rescuers one by one, looking good in those shades. It's hugs all round.
16.50 Daniel Herrera appears! Welcome back. He's smiling but the tears are streaming down his mother's face. Now he waits for the customary hug from President Pinera.
16.47 Quick reminder - we are waiting for the 16th miner of 33. The rescue operation is almost half way to completion. It's all running smoothly so far
16.45 President Pinera says the operation will continue without rest until all miners are free. One miner an hour has appeared on average so far but there are reports that the speed of the rescue might increase with one man to be brought to the surface every 40 minutes.
16.42 Daniel Herrera, a lorry driver as well as a miner, is making his way to the surface. Shouldn't be long for his family now.
16.38 Fans of the Chilean miners and fans of the computer hero Mario rejoice! Check out this image.
16.21 Daniel Herrera will be the sixteenth man to be rescued
16.10 President Pinera greets Victor Segovia, telling him that he is about to start out on a "new life".
15:51 Victor Segovia will be getting into the rescue pod in the next few minutes: miner number 15.
15:46 In case you're just a little envious of how healthy these men look - and let's face it, who isn't? - a website's published a guide to what they ate.
15:44 How long for the first bit of rock brought up from the mine goes on eBay?
15:42 More famous tweeters have been commenting on the rescues, including Keith Chegwin, Calum Best and Gok Wan.
15:37 Alfredo Cooper, the Chilean president's Protestant chaplain, described today's events as "a miracle", definitively so as a drill bit had been deflected from its original route when it found the miners' refuge.
15:34 With 33-year-old mechanic Victor Zamora's emergence into the sunlight, 14 men have now been saved. What looks like his wife is wiping away tears as she waits to hug him. And there it is. A long, deeply emotional embrace. This is a man who left his home when it was struck by an earthquake, then got trapped in a mine. On the day of the collapse, he should have been at the surface.
15:27 In case you've forgotten, or never knew, the San Jose mine is about 25 miles outside Copiapo, a town about 40 miles inland from the Pacific coast of Chile. Copiapo's co-ordinates are 27.20 south by 70.23 west, which puts it roughly on an east-west level with Johannesburg and Brisbane.
15:19 Once the last miner comes up, bells will be rung along the length of the country; from Arica in the north to Punta Arenas in the south, around 2,700 miles.
15:16 The Phoenix has landed. Back in the underground refuge at least. Victor Zamora is next in line.
15:13 Sebastian Pinera, the Chilean president, says the country has come through a night in which "life defeated death, when hope defeated anguish. A night which made us feel more human, more alive."
15:09 Evo Morales, the Bolivian president, is still around. He's just promised a new job - presumably in Bolivia - to Carlos Mamani, his citizen and the only foreigner to be trapped down the mine.
15:06 The Phoenix Two rescue capsule is based on something called the "Dahlbusch Bomb", a device which had its finest hour in "The Miracle of Lengede" in 1963, where 11 West German miners were pulled alive from a mine collapse.
14:57 Barrios was only a part-time miner who also drives a taxi. He's a horse racing fan who complained to his family about interference from psychologists.
14:54 Carlos Barrios, 27, becomes the 13th saved man.
14:44 The rescued men are supposed to spend two days in hospital now before they?re released. I hope the wards have stocked up on beer.
14:41 Carlos Barrios is loaded into the bullet-shaped capsule, and is shot to the surface in slow motion.
14:39 A shift change at the mine brings about 30 policemen marching through the camp, singing as they go. Apparently this is normal.
14:14 And that makes a dozen. The 34-year-old shakes hands, hugs and high fives his rescuers.
14:11 Edison Pena, who ran three miles underground every day to keep him sane, is on his way to the surface.
13:54 One of the reasons the tunnel to the miners was so tough to dig was that it was drilled through granite - one of the hardest rocks on earth - studded with quartz - one of the most abrasive.
13:47 Aunt of Jimmy Sanchez, the youngest of the group who was pulled out earlier, says he's "completely fine" and will now go back to college to continue studying.
13:33 Jorge Galleguillos, 56, becomes 11th miner saved. And he's grown a beard while underground. That's a third of the men rescued. And the first beard.
13:32 Bolivian president Evo Morales, himself a former miner, arrives at the scene.
13:09 Chile is building towards a huge party - bottles have already been uncorked at Camp Hope and every schoolchild has been given the day off.
12:59 The Phoenix Two rescue capsule reenters the rock, dangling from its cable which was brought from Germany specifically for the purpose.
12:56 With his safety helmet tipped at a jaunty angle, Vega gives two thumbs up before embracing his wife for a long time, then shows his tee-shirt which is emblazoned with ?Gracias Senor? or ?Thank you God?.
12:52 Alex Vega surfaces - chewing gum - and becomes the 10th miner saved.
12:50 ?Chilean Max Clifford? attempting to get all the miners to sell story in one go to maximise cash, BBC claims.
12:47 Mining minister Laurence Golborne tweets that the rescues are coming faster. They've gone from around an hour each to between 45 and 50 minutes.
12:36 Never before have trapped miners survived for so long.
12:34 Next person out will be Alex Vega, 31.
12:30 Some clever person redesigns an image from a classic computer mining game to include the Phoenix Two rescue capsule.
12:20 Lucy Herrera, the mother of Daniel Herrera, who is expected to be the 16th miner to be saved, tells the BBC World Service she hopes she won't break down in tears in front of him. "I am actually really calm. I thought I would be more nervous, but I have surprised myself. I'm just waiting my turn."
12:15 Estimates have put the cost of the rescue at £12.6m.
12:13 And Gomez is far from the only one praying: the Pope has offered prayers for the safe recovery of all the Chilean miners.
12:04 Gomez hugs wife and drops to his knees to offer thanks for his survival. Bizarrely, the miner, who lost three fingers on one hand, previously survived 11 days trapped in a shipping container after stowing away on a ship, and stayed alive by drinking water from a shoe and nibbling a piece of chocolate.
11.59 Applause from the rescuers and a thumbs up to Mrs Ramirez, as the capsule reemerges. Mario Gomez is the ninth miner rescued.