So, Celtic book their place in the Scottish Cup final and a meeting with Motherwell after Brendan Rodgers' side proved too strong for 10-man Rangers at Hampden.

Highlights of today's semi-final will be on Sportscene tonight, on BBC One Scotland at 22:30.

We'll have highlights on our site after that programme and further reaction from Hampden in due course.

Here is a link to Martin Dowden's match report from the national stadium.

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Image source, Getty Images

More from Rangers manager Graeme Murty, who has been speaking to the rest of the media after his side's limp performance.

"There are lots of things to look at," he said. "In the raw emotion of it now, we didn't put them under enough pressure; we allowed them to play far too easily. All four goals were easily avoidable through just basic, good defending.

"Then in the second half, we gave them a penalty and a sending-off which makes their job far, far easier.

"We were just passive. I don't know why. I asked them to get into a shape and a structure in order to go and press. But when it comes to one against one, you have to actually go and get up closer to your opponent than we did in the first period.

"We had really good opportunities to claw something back from the game and we haven't managed to do it. I said we had to be clinical in both boxes but I don't think we managed to do that at all.

"Craig [Gordon] made a couple of good saves but we should be scoring at least one. We were not worthy of getting anything from the game today."

Speaking to BBC Scotland, Celtic manager Brendan Rodgers: “I was very proud of the team. It was always going to be a difficult game. There’s always that edge but I thought we controlled it well in the first half. They looked like they were trying to block the middle but that gave us space down the side.

“From the first goal we had really good control throughout the game.

“The middle of the park was closed up, Rangers had gone with three flat midfield players. The possibilities are on the outside and we worked that well.

“That’s something I have said to them. I’m always looking to push them, but they bring the real edge to it. They have inspired the supporters in my time here. We have a way of playing that we know can win games.

"The supporters were incredible for us and can look forward to the 19th of May.

“Tom Rogic shows his strength and skill to finish, he was very good. He scores big goals in big games.

“The important thing now is to close up the league. The final will be a tough game, you saw Motherwell yesterday [against Aberdeen]. They work hard and won’t make it easy."

Image source, Getty Images

Speaking to Sky Sports, Rangers manager Graeme Murty: "I’m frustrated, I didn’t think we turned up in the first half. The sending off changed the nature of what we wanted to do second half.

“We just didn’t get close to anyone, it took half an hour to make a tackle.

“I will look at myself and learn from it. It’s too raw right now, all that will happen now is conflict.

“Andy [Halliday] was frustrated, he’s been taken off before half time. I’ll speak to him during the week.

Image source, Reuters

“I’ll apologise for the first half. It’s a lonely place out there, but we need to make sure this doesn’t happen again.

"I won’t talk about my role at this time, it’s not about me."

Andy: Rangers are a shambles from the manager's office all the way down.

Alan: Rangers will finish 4th [in the league] on that showing.

Kim: Amazing result, well done you Bhoys!

Celtic midfielder Scott Brown, speaking on Sky Sports, rubbed some salt in the wound by referring to reports the Rangers players cheered when they were drawn against Celtic.

He said: "They can cheer as much as they want, I don’t think they’ll be cheering tonight.

“We knew from start to finish we were going to dominate the game. We just knew as soon as we turned up that we’d win it."

And two-goal hero Moussa Dembele added: "We knew if we play at our level we’re the best team in the country and we showed that again today."

Image source, SNS

Martin Dowden
BBC Sport Scotland at Hampden

The scoreline says it all and it could have been more.

This was an absolute canter for Celtic who were light years ahead of their Glasgow rivals on this occasion.

On this evidence any suggestion that the gap has closed has to be extinguished.

Rangers got it all wrong today. It was a painful, painful afternoon for their supporters in stark contrast to those wearing green and white.

Yet again, Brendan Rodgers’ side has delivered when it mattered.

Image source, SNS

Pat Bonner
Former Celtic goalkeeper on BBC Sportsound

David McCartney: At least Motherwell will give Celtic a game in the final that was like a training session. Very poor show from Rangers.

Paul Smith: Training session for Celtic

Celtic are through to their 56th Scottish Cup final. They have won 37 of the previous 55, the latest being last year's 2-1 triumph over Aberdeen.

Will captain Scott Brown be lifting the trophy again on 19 May? Only Motherwell can stop the 'double Treble' now, with Celtic within three points of a seventh consecutive league title.

Image source, SNS

Billy Dodds
Former Rangers striker on Sportsound

Three minutes of added time at Hampden. Bruno Alves is back on after receiving treatment.

Rangers substitute Bruno Alves is down nursing what looks like a leg injury. The Portuguese is limping to the sidelines...

Callum McGregor, from a Kieran Tierney cutback, sends a shot narrowly over the bar as he looks for his second and Celtic's fifth goal of the day.

Pat Bonner
Former Celtic goalkeeper on BBC Sportsound

Patrick Roberts twists and turns as he tries to evade a couple of Rangers defenders but concedes a throw-in. Many of the Rangers supporters are heading for the exits as we approach the final five minutes.

Rangers manager Graeme Murty, from his technical area, looks down at the Hampden turf. He, like the Rangers supporters in the stands, looks stunned.

Leigh Griffiths comes on for Moussa Dembele for the final 10 minutes against 10-man Rangers.

Billy Dodds
Former Rangers striker on Sportsound