So, a good win for Andy Murray. He will next face either American John Isner or Serbia's Viktor Troicki. You can watch those two duke it out by continuing to follow this stream. Goodbye.

Piers Newbery
BBC Sport at Queen's

"After two clinical sets from Muller that goes down as a very good win for Murray, and ideal preparation for the weeks ahead. It was interesting to see his change in fortunes arise in the tie-break thanks to markedly improved footwork and an eagerness to step in and attack returns, both hallmarks of coach Jonas Bjorkman's game.

"If he is going to win a fourth Queens Club title this weekend, there is every chance Murray will need to see off another one or two big servers."

Andy Murray on BBC Two: "I hit a good passing shot at 1-0 in the tie-break, but those don't always go in so that was a bit lucky. I started to read the serve a bit better at the end of the tie-break and that was when the match changed.

"It's always tough when you're behind and I wasn't getting many changes at the end, but at the end I started to return better and relaxed a bit more, and I played some good tennis. Hopefully I can take that form into the semi-finals.

"It will be a tricky match whoever I face. I'm in a good place, physically I feel good."

Murray steers a passing shot that Muller can only get the frame of his racket on. A big serve is flopped into the net, before a magnificent point at 30-15 - a superb drop shot from Murray is somehow chased down by Muller and dinked diagonally back over the tape, but Murray is ready and hits a forehand into the open court to bring up two match points. Murray takes it at the first time of asking with a big serve that Muller can't get back, and Murray is through to the semi-finals of Queen's.

Image source, Reuters

Murray is hurling himself after every ball here - he almost ends up running into the stands in his fruitless pursuit of a Muller volley. But from 30-0 up, the Luxembourger hits a couple of ropey volleys to subside to 30-40 and match point. He's not giving up though - two aces drag him out of the mire and another big serve seals a teak-tough hold. Murray will have to serve it out.

Image source, Reuters

No messing from Murray - he belts a couple of forehands into the corner to move one game away from victory.

Signature Murray - a gorgeous whipped lob off one foot sails in a perfect aesthetic arc over Muller's head and plops delightfully in the corner. But Muller isn't giving this one up without a fight - some big serves and heavy forehands keep him in the hunt.

A nice cat-and-mouse rally on the first point ends with a frantically back-pedalling Muller firing a Murray lob into the tramlines. He can't get into the Murray service games at the moment - is there another twist left in this match now?

He's still not happy, Andy Murray - a couple of missed chances on the Muller serve get him screaming at himself again. Muller has slightly recovered his composure here and a nice pick-up closes out the game to keep him within touching distance.

Image source, Reuters

Muller was picking off volleys like a chameleon catching flies earlier, but his golden touch at the net has deserted him - he can't manage to scoop the ball off his shoelaces, and that's all the encouragement Murray needs, as he closes out another comfortable hold.

Piers Newbery
BBC Sport at Queen's

"As the sun dips down towards the back of the stand, Murray finally gets the upper hand. Spurred on by the vocal presence of coach Jonas Bjorkman and trainer Matt Little on the sidelines, the Briton is suddenly bouncing around and threatening the formerly invulnerable Muller serve.

"And if he can see this out, it will leave potential semi-final opponents John Isner and Viktor Troicki to come out and try to get the job done before darkness falls. Advantage Murray."

This hasn't been the greatest performance from Murray, but it has showcased some of the virtues which make him such a formidable champion. He clung to Muller like a limpet and now he is slowly sucking the self-belief out of his opponent. Nothing illustrates that better than when Muller, who hasn't missed a volley all afternoon, suddenly errs at the net, prodding a limp push long to bring up two break points.

Muller saves them with big first serves, and then when recovers a third break point with another howitzer delivery. The crowd are being treated to the full repertoire of Murray's interior monologue, and with a loud 'Noo!' from the Scot, a relived Muller closes out the game.

Image source, EPA

The psychological momentum in this match has shifted decisively and Muller has to be careful he doesn't get swept away on the tidal wave here. A wide approach and a faltering return from Muller give Murray a simple hold.

Image source, Reuters

John Lloyd
Former British number one on BBC Two

"Murray is back in business. He's looking absolutely brilliant right now and has gone up another gear."

So, on we go - can Muller dig deep and get over the disappointment of losing that set? It's Murray who has the spring in his step now. Muller hooks a forehand into the tramlines to bring up 15-30, and then Murray stings a return which Muller can't shovel back from the baseline. Two break points, and Murray takes the second when he batters a second serve back past the forlorn Muller. On Easy Street now?

Image source, Getty Images

The draw has rather opened up for these two players after a week that has proved just how easily the big names can be upset on grass.

Rafael Nadal was first through the exit door, beaten by Alexandr Dolgopolov, followed by Stanislas Wawrinka, who lost to Kevin Anderson.

Muller himself put away last year's champion Grigor Dimitrov, and US Open winner Marin Cilic was ousted by Viktor Troicki.

In fact, apart from Murray, only one other of the eight seeds that started the tournament remains: seventh seed Gilles Simon, who beat third seed Milos Raonic earlier today.

A hopeless lob from Muller allows Murray to dink the ball into the empty court and bring up four set points. He takes the first when Muller nets a backhand, and the British number one is right back in this match!

Image source, Reuters

Murray is fractionally wide of the sideline with a stretching return, but Muller then gets an attempted smash horribly wrong to hand the initiative back to the Scot.

Muller wallops a forehand millimetres long - upheld on review, much to the delight of the well-refreshed Queen's crowd. But Muller gets one of the mini-breaks back with a good volley.

A brilliant pass from Murray earns him a mini-break, and then he shows great instincts to hunt down a volley. Murray in charge.