Hamilton takes fourth world title - making him most successful British driver of all time
He joins Vettel and Alain Prost on four championships
Briton finishes ninth after colliding with Vettel on opening lap
Verstappen wins race, Vettel battles back to 4th
Ricciardo, Hulkenberg, Hartley, Ericsson, Sainz out
Listen again, via our BBC Radio 5 live commentary, to the moment Lewis Hamilton sealed his fourth world title.
Listen to the moment Lewis Hamilton sealed his fourth world title.
He won't get all the headlines, but it was a masterful performance from Max Verstappen, who managed to avoid the first lap drama going on around him involving Lewis Hamilton and Sebastian Vettel.
Verstappen wins it by a margin of almost 20 seconds.
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Deji Guerrero: Congratulations to Lewis Hamilton for the 4th Title; time to start preparing for the next title to catch Fangio and surpass Vettel
David Hudson: Surely Lewis Hamilton takes this year's BBC Sports Personality of the Year award? Well done Lewis!
James Ayres: Congratulations to Lewis Hamilton 4 time World Champion! Desperate attempts by Vettel today to stop him but he did it!
This is the final result from the Mexican Grand Prix.
Red Bull win a race for the third time this season, with Verstappen's second success of the year after also triumphing in Malaysia.
Valtteri Bottas' second is his best finish in four races, while Kimi Raikkonen came third for a second successive race.
Force India have a great day as Esteban Ocon takes fifth, with Sergio Perez seventh. Williams' Lance Stroll's position of sixth is his second best performance of the season, behind the third-place he obtained in Azerbaijan.
Kevin Magnussen gets a points finish in his Haas for only the second time in 10 races, while Fernando Alonso ended 10th, only the third time he has come in the top 10 in 2017.
Image source, F1Lewis Hamilton wins the world title for a fourth time
Allan McNish
Formula 1 analyst on BBC Radio 5 live sports extra
The second half of the season has stood out for Lewis Hamilton. It was a tricky first half, Mercedes were not the quickest but there can only be one world champion and he is a very deserved one.
I am not sure about next season but in the next couple of season there is a very high chance there could be another title.
Hamilton has won because he has been a lot more consistent. Ferrari dropped the ball due to reliability and driver error.
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Rob Walters: Congratulations Lewis Hamilton. You'll probably never read this, but you are an amazing role model to so many.
John Wilkinson: Got to be a knighthood now for Lewis, surely?
Ashley Wilkinson: Time for everyone to truly appreciate the greatest British sportsman of his generation. Congrats Lewis Hamilton - 4x World Chanpion
Mercedes' non-executive director Niki Lauda, a three-time world champion, is told that Lewis Hamilton has now won the world title more times than he did.
"Thank God," Lauda responds. "Lewis won it, he deserves it and it has been the best driving than he has ever done before."
Asked about the first-lap incident where Vettel hit Hamilton, Lauda added: "I don't know why Sebastian drove so aggressively to destroy his race and Lewis'. Lewis was in front and he (Vettel) hit him with his front wing, I just don't understand it.
"I'm more proud than the other three world championships we won together because this year was very competitive and today you saw the outstanding win of Max Verstappen."
Third-placed Kimi Raikkonen says: "The initial start wasn't too bad but all of the guys I was next to got a massive tow and I was left alone.
"It was a disaster after that but we had some patience and we had enough speed to improve."
Lewis Hamilton wins the world title for a fourth time
Valtteri Bottas, who finishes second in Mexico for a first podium finish in four races, says: "First of all big congratulations to Lewis and our team for winning both titles
"It is nice to be part of that. Red Bull was too quick. We tried everything we could and couldn't catch them."
Allan McNish
Formula 1 analyst on BBC Radio 5 live sports extra
It was a challenge in the beginning part of year but Hamilton has won five of the last seven races.
The only other two victories have not been Vettel but Max Verstappen.
It was a tough one. When you have the might of Ferrari as a challenge you know you have to step up but Hamilton and Mercedes stepped up that game.
Race winner Max Verstappen says: "The start was very crucial, I went around the outside and from then on I was just looking after the car and the tyres.
"Big thanks to Red Bull, without them it was not possible. After last week (when a five-second penalty denied him third place), it is a perfect race, it was great."
Image source, Getty ImagesMore from Lewis Hamilton: "It doesn't feel real. It is not the kind of race I wanted, 40 seconds behind, but I never gave up. That is what is important and in my heart. I am grateful for today."
Image source, Getty ImagesLewis Hamilton wins the world title for a fourth time
World champion Lewis Hamilton says: "Viva Mexico. Wow.
"I just want to say a big thank you to everyone who came out, hopefully we gave them a good race. The Mexican fans are the best around the world and you guys create this atmosphere.
"I had a good a start, I don't know what happened on turn three I gave him (Sebastian Vettel) plenty of room. A big thank you to my family, my team, Mercedes have been incredible for these last five years."
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Jayne Morgan: Get in Lewis. Well deserved.
Josh Brigham: The Greatest British Sportsman of our Time, Lewis Hamilton wins his 4th World Championship Title, unprecedented.
Megan Walton: Lost track of how many heart attacks I had during that race.
Lewis Hamilton wins the world title for a fourth time
Mercedes team boss Toto Wolff on BBC Radio 5 live: "I hated the race but I am super happy now. He (Lewis Hamilton) has achieved it and the team has won. This is the most important.
"It was a bizarre accident (involving Sebastian Vettel and Hamilton). It wasn't looked at which is even more bizarre but it is most important that he has done it."
Image source, Getty ImagesLewis Hamilton wins the world title for a fourth time
Some celebratory messages for Lewis Hamilton.
Mercedes to Hamilton: "Get in there. Champion of the world."
Toto Wolff: "Not the race you wanted, but who cares."
Niki Lauda: "Thank you, thank you, thank you, thank you. Four times thank you."
Image source, Getty Images
Tom Clarkson
BBC Radio 5 live sports extra commentator in Mexico City
High fives all round at Mercedes. Toto Wolff is smiling like a Cheshire cat. It is the first time he has shown any emotion in this grand prix.
Jack Nicholls
Radio 5 live Formula 1 commentator
Hamilton, a four time world champion, puts his head in his hands.