Cook 244* - highest score v Australia
Smith drops Cook on 66 & 153
Cook & Broad (56) add 100 for 9th wkt
Root 61, Woakes 26, Bairstow 22
Lyon, Hazlewood & Cummins - 3 wkts
Australia lead 3-0 in five-Test series
Alastair Cook started his innings as the 9th highest run-scorer in Test cricket. He's now 6th, having surpassed Mahela Jaywardene, Shivnarine Chanderpaul and Brian Lara.
Kumar Sangakkara, you're next...
Australia coach Darren Lehmann, speaking to ABC: "Cook has been under some pressure but he responded really well today. We would have loved to have that (Cook's innings) in our first innings. They showed the application required to bat a long time. There are no demons in the pitch but reverse swing. The way he played is why he has almost 12,000 Test runs.
Asked if he believes his side can still win the game, Lehmann said: "We would have to bowl them out quite cheaply. It will take a long time to get past them. Our job is to bat a lot of overs.
"The batters have got to stand up and it is a great challenge for them. You never say never but we are a long way behind in the game. It is tough to see a scenario other than a draw or England win."
Ah yes, Broad's dismissal. The number 10 might count himself unlucky not to still be out there.
He spliced away a short ball towards third man, with Usman Khawaja running in and taking a diving catch.
Or did he? The soft signal on the field was out, but replays showed the ball popped back out of Khawaja's hands before he did or didn't gather it cleanly under his chest as he fell to the ground.
A touch of controversy and more scrutiny on the umpires in this series.
Image source, Getty Images
BBC Test Match Special
England's Stuart Broad: "It was amazing, very special to be out there for Cooky's 200. I don't think the Barmy Army stopped singing. It is awesome and helps as a batsman.
"We had a bit of fun but I was careful not to get Chef too far out of his bubble. He has such a good zone and didn't want to do something too daft.
On decision from the umpire over the catch for his dismissal, Broad said: "How do I not get a fine? I think it was tricky to tell from 80 yards away. Once the soft decision was out it is tricky to overturn."
Image source, ReutersMake that two days to England. After winning three straight session for the first time in the series on day two, England have done it again on day three.
And that's thanks to Alastair Cook - the opener converting his unbeaten century into an unbeaten double century in sublime fashion.
Along the way he overtook some of the greats in the game in various categories and has put England into a really strong position - 491-9 and a lead of 164 runs.
There were some mishaps along the way - more on that soon - but Stuart Broad combined brilliantly in a 100 partnership with Cook, the number 10 adding a vital 56 of his own.
Stephan Shemilt
BBC Sport in Melbourne
I kid you not. After the day his side had, Australia coach Darren Lehmann was briefly locked inside his press conference.
Image source, BBC Sport#bbccricket
It will only be when Cook retires that he will get the plaudits he deserves, and will be accepted as one of the all-time greats.
Adrian Bennett, Gloucestershire
BBC Test Match Special
Image source, PAEngland's Alastair Cook: "Last night was quite an emotional 20 minutes from where I have been. Getting a hundred didn't count for much unless I backed it up today. At Perth I said I was embarrassed, I know it is late but it is nice to contribute to a good day.
"In all three games we have put Australia under pressure in two or three sessions and we haven't been able to back it up. Here even halfway through the afternoon we were in danger of only getting a 60-run lead and I thought we needed more than that.
"Broady played really well. It was good to have bit of a partnership to get us up to a good lead."
Michael Vaughan
Ex-England captain on BBC Test Match Special
Image source, Getty ImagesFrom the minute Cook walked out he played good strokes and his bat has looked very wide. He played with the strength of mind we know he has got.
His mind has always been his strength but what impressed me is the technical attacking ability rather than looking to survive. It just shows, no matter how many games you play, you do lose confidence.
Elsewhere, Jonny Bairstow played a poor shot to edge Nathan Lyon behind and Chris Woakes made a very scratchy but useful 26.
For now, though, it matters little thanks to Alastair Cook's supreme effort.
Text 81111
Saying “I’ll go to bed when Cook gets out” can often lead to a severe lack of sleep. Nice one, Chef. Night all.
Adam in Newbury.
Ed Smith
Ex-England batsman on BBC Test Match Special
What have we learned about Alastair Cook today? Not a lot. He is the best concentrator to have played for England in my lifetime. He played with incredible serenity and calm. Cook the concentrator, Cook the accumulator of runs.
Next up in nervy moments for England today was the strange innings of Moeen Ali.
Clearly short of confidence and mindful that he's got out playing defensively to Lyon this series, Moeen counter-attacked, smacking the spinner around to reach 20.
But it was there the fun ended - Moeen trying to clatter Lyon over cover but only finding Shaun Marsh, who took a fine catch over his head.
For some, it was the right approach but wrong execution, given Moeen might well have not even got to 20 by playing meekly.
For others, it was a rash and irresponsible innings in the context of the game as it left England 307-6 and still 20 runs behind Australia at the time.
Will his intent at least help to spark something for the out-of-sorts Moeen?
Image source, ReutersMichael Vaughan
Ex-England captain on BBC Test Match Special
It was a strange one. It was a massive inside edge, how Dawid Malan has not felt that I am not sure.
Also the umpire got it wrong on two counts. He hasn't noticed the inside edge and hasn't noticed it was outside the line.
A quick glance at the score might suggest it's been serene progress for England but there were plenty of nervy moments along the way on day three.
Joe Root looked on course for a big score but fell into a familiar trap, miscuing a pull shot straight to Nathan Lyon, who was set back for that shot. Root out for 61 and more questions about his conversion rate.
Dawid Malan then got a start but was dismissed in bizarre fashion. He was given out lbw to Josh Hazlewood but replays showed he got a thickish inside edge onto his pads.
After consultation with Cook, Malan chose not to review - the second time in two days an England batsman has not reviewed an lbw decision that would've been overturned after James Vince got a thinner nick onto his pads on day two.
Image source, AFPMichael Vaughan
Ex-England captain on BBC Test Match Special
It has been one of Alastair Cook's best innings because I have not seen him hit the ball down the ground so hard. Whether it is the pitch or the absence of Mitchell Starc only he can answer.
Alastair Cook started the day unbeaten on 104 and added another 140 runs today in emphatic fashion.
Steve Smith, who dropped Cook on 66 yesterday, spilled him again on 153 and both times the opener has really made a tired Australia pay.
Huge credit to Stuart Broad too. He got the customary short ball welcome but stood tall and then tucked in when his eye was in, compiling a fine 56 in a thoroughly entertaining stand of exactly 100 with Cook.
Image source, AFP
Andrew Samson
BBC Test Match Special statistician
Alastair Cook went from 9th highest run-scorer in Tests to 6th in 24 hours, passing Mahela Jayawardene, Shivnarine Chanderpaul and Brian Lara.
Image source, Getty ImagesYes you're reading this right. England have a first innings lead of 164 and Alastair Cook has scored his fifth Test double hundred, ending the day 244 not out.
England's former captain has batted all day and has done so brilliantly. He has broken a host of records in this innings and is now in fact England's leading run scorer in the series, despite a dismal first three Tests.
England lost Joe Root early despite the skipper passing 50 again and Jonny Bairstow, Dawid Malan and Moeen Ali all made starts but got out.
England were still trailing when Moeen was out but first Chris Woakes and then an excellent 56 from Stuart Broad has taken England into a lead.
Broad was controversially given out late on when it was unclear whether Usman Khawaja held onto a catch in the deep, meaning England closed on 491-9.
For the first time in this series England have a real chance of victory.
Hello to those of you just waking up, perhaps getting ready for your first day of work after Christmas.
It's good news, England fans. Play has just ended for the day but stay tuned for plenty of recaps and reaction...