Well, that was quite a night.

A wonderful defensive display from Aberdeen with two ruthless finishes that sunk Rangers, who had so much possession but did so little with it.

Bookings galore at Ibrox, the most noteworthy given to Dons skipper Graeme Shinnie, who now misses their semi-final date with Celtic.

Hearts had something of a rocky route to the last four, coming from behind, missing a penalty, then surviving two late shouts for a Partick Thistle spot-kick in Gorgie. But they'll be feeling very good about themselves and their cup prospects with second-tier Inverness their semi-final opposition.

Sporscene's less than half an hour away - watch all the highlights from 23:00 on the new BBC Scotland channel.

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Rangers manager Steven Gerrard is understandably none too happy. He tells Rangers TV: "It’s a huge blow, this was a huge game for the club. For myself, the players, all the fans. We’ve let the supporters down, I take full responsibility for it. We were nowhere near good enough, I thought the best team won.

"We started the game extremely poor, and we never got much better from there."

McInnes is "gutted" for captain Graeme Shinnie, who misses the semi-final after being booked tonight.

"I’ve had this conversation before, we’ve had two replays and I always feel there should be some sort of concession when you play those two extra games," he added.

"It’s a blow for us, a blow for wee Shinnie, but we’ve had to deal without good players before. We’ll try and get into a final and hopefully Shinnie will get his hands on that trophy."

Aberdeen manager Derek McInnes on BBC Radio Scotland: "We can't come here and take Rangers on in a possession-based game. They’ve spent a small fortune putting that team together and they’re a good side and we’ve seen often enough how free-flowing they can be if they get space to operate.

"We didn’t need to make it that type of game and our best way of getting the result was we allowed certain players to have the ball and other players to have it in certain areas of the pitch.

"But we still have to have the concentration and determination one-v-ones to see the job out. Also having to try and counter well.

"What we did do was get a brilliant start, McGinn take advantage of the opportunity and a lovely calm finish and half-time came at a good time.

"Once the second goal goes in, a great move, I felt it knocked the stuffing out of Rangers and it all became a bit desperate for them. We executed the plan very well and the players deserve real credit."

Partick Thistle goal-scorer Scott McDonald discusses those late penalty shouts at Tynecastle.

"Couple of contentious decisions we're not pleased about. We felt at least one of them should have been a penalty. It was a big call late on," the Australian said.

"The first one when Miles Storey goes through, this is where we have a problem and where I talk about making referees have to make a decision. Why does he have to go down for it to be a penalty? That's why we have the issues we have - players have to fall over to actually get the foul.

"Miles is clear the other side of Christophe Berra and gets pulled back two or three times. Bobby Madden still waves play-on. They're the ones you should get but don't because you don't go down."

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Partick Thistle boss Gary Caldwell has an interesting view of how Hearts goal-scorer Uche Ikpeazu operates.

"For two games we’ve defended really well against Ikpeazu. He's clever in how he plays - the strongest man in the world in some situations and in others he goes down like my little girl in the park," Caldwell said.

On Thistle's two late penalty appeals, Caldwell said he'd watched both back and spoken to referee Bobby Madden.

"It’s very difficult for the referee.The first one is not a penalty and I’ve apologised to [Madden] because I’m claiming it during the game.

"The second one he said he was unsure and when I’ve watched it back, it was a penalty. It was a disappointment we didn’t get that opportunity to take it to extra-time because if we did, I think we’d have been the stronger team, we were in the ascendancy, we had energy and the crowd might have turned against Hearts but it wasn’t to be. It was a great effort and we have to just take that from the game.

"We have stood toe-to-toe for two games with a team that should be top four in this country and given them a real fright."

Neil McCann
Former Rangers winger on BBC Sportsound

Willie Miller
Former Scotland defender on BBC Radio Scotland

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Neil McCann
Former Rangers winger on BBC Sportsound

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Hearts will come up against one of the club's great heroes in the semi-finals. Inverness are managed by John Robertson, who scored over 100 goals for the club and a record 27 against Edinburgh rivals Hibs.

Hearts thumped Inverness in the League Cup way back at the start of the season but Levein says "they're a much stronger outfit now".

"People will say we are strong favourites but I know Robbo will have his team ready, they'll be well-organised and they'll have a go for sure," he added

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Hearts manager Craig Levein tells BBC Radio Scotland that Uche Ikpeazu is unlikely to be allowed to take another penalty after his poor spot-kick was easily saved.

The big striker scored earlier in the game and won the penalty that would have put Hearts 3-1 up in the second half.

"He had an agreement that if he won a penalty he'd get to take it," Levein said.

"Unless the other 10 players get injured, I would doubt [that Ikpeazu will take another]."

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Aberdeen and Hearts fans, you'll want to get the new BBC Scotland channel on the box in just over an hour's time.

Jonathan Sutherland presents highlights from both semi-finals at 23:00.

That's the second time this season Aberdeen have knocked Rangers out of a cup.

They also beat Steven Gerrard's side 1-0 in their Hampden League Cup semi-final in October.

The only sour note for Derek McInnes' men was the yellow card shown to captain Graeme Shinnie, meaning he will miss the Scottish Cup semi-final against Celtic.

And away from all the Scottish Cup tumult, Ross County have strengthened their grip on top spot in the Championship.

They're very much in pole position to win the title after tonight's 2-1 win over Falkirk took them 11 points clear.

Allan Preston
BBC Scotland summariser on Sportsound

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So, here's confirmation of the semi-final line-up. The matches will be played in a month's time on 13 and 14 April.

Hearts v Inverness CT

Aberdeen v Celtic

There are fewer than 1,000 away supporters crammed into a sliver of Ibrox, but boy, are they making themselves heard.

This is a glorious, raucous night for Aberdeen in Glasgow. Resolute at the back, deadly when it mattered, they've got the better of Rangers again.

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Job done for Hearts after a sticky tie against Partick Thistle in awful weather.

They're into their second semi-final of the season. A trip to Hampden beckons now, and they'll fancy their chances against second-tier Inverness.

What a win for Aberdeen! A tactical masterclass from Derek McInnes. The Dons are into the Scottish Cup semi-finals, where they'll meet Celtic, and have beaten Rangers for the third time in Glasgow this season.

For Rangers, their chances of silverware in Steven Gerrard's first season in charge rest on overhauling an eight-point Scottish Premiership deficit to their Old Firm rivals.

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Phenomenal ball-carry from Graeme Shinnie, who runs his team out of trouble, runs between three Rangers players and is cynically clipped by Steven Davis. Booking for the Rangers man.

Aberdeen are all-but home and dry.