Image source, Huw Evans Picture Agency

These are heady times for Glasgow and their followers.

Never before have they breathed this rarefied air at the summit of Europe. Victory today sets up an intoxicating date with Toulon or Benetton on 19 May at Dublin's Aviva Stadium.

Franco Smith has built a team capable of winning in several ways, and with a big chance to clinch Scotland's first continental silverware.

That brings our coverage to an end today. Thanks for your company, and enjoy the rest of your weekend.

Glasgow Warriors head coach Franco Smith tells BT Sport. "The Scarlets threw everything at us tonight, the crowd was immense. For us to handle the pressure we put on ourselves in the first half was fantastic.

"We felt a little bit nervous, even guys who have played Test-match rugby. Lesson learned, we went back to the process, and I’m looking forward to seeing what we take out of this review.

"Ollie Smith got another hand to the ball. If he didn’t, maybe it’s a different story. We were staring at the video, I was very nervous, but the fact he got another touch made a difference.

"Benetton have been playing well lately, have had some good away games in South Africa. Toulon are a consistent power and have some star-studded players. It’s going to be interesting, we will be sitting watching."

Peter Wright
Former Scotland prop on BBC Radio Scotland

What Glasgow said at half-time worked. Bringing on Johnny Matthews worked, because they couldn't buy a line-out.

There are massive decisions for Franco Smith next week, picking the best team for Munster.

A sore one for the Scarlets, literally, who were 14-7 up at half-time and looking pretty tasty.

They had chances to set up a grandstand finale, too, but heroic Glasgow defending denied Kieran Hardy and Ryan Conbeer.

I wonder whether they'll feel aggrieved Ollie Smith didn't see yellow, and Scarlets didn't get a penalty try, for that attempted interception in the final quarter.

And that spree of injuries - Javan Sebastian, Johnny Williams, Morgan Jones and then Vaea Fifita - eventually told.

With no URC play-off involvement, their season ends here.

Colin Gregor
Former Glasgow Warriors back on BBC Radio Scotland

That period around 65 minutes, Glasgow had to defend, deal with line-outs, deal with scrums, deal with penalties and they did that so so well.

Then the icing on the cake - an intricate move at the back of a line-out and it's a really good evening's work.

Gareth Delve
Former Wales international on BBC Radio Wales

Scarlets had a little bit of bad luck, losing Javan Sebastian and Johnny Williams early on.

They ran out of steam at the wrong times.

I'm sure there will be plenty of talk about that knock-on by Ollie Smith too.

Peter Wright
Former Scotland prop on BBC Radio Scotland

Glasgow have got a massive game next week against Munster in the URC play-offs.

You would potentially say Toulon will win the other Challenge Cup semi-final against Benetton.

And what a final that would be - Glasgow against Toulon. Absolutely brilliant!

Before that, though, Glasgow must negotiate another knockout extravaganza.

They host Munster in the quarter-finals of the URC.

What an exhilarating end to the season.

Gareth Delve
Former Wales international on BBC Radio Wales

Glasgow fixed a lot of those errors from the first half, had a bit more patience in attack and ground down a wounded Scarlets.

Glasgow are worthy winners.

Glasgow will face last year's runners-up Toulon or first-time semi-finalists Benetton in next month's showpiece.

Those two meet tomorrow on the Cote d'Azur.

Image source, Huw Evans Picture Agency

Glasgow's player of the match Jack Dempsey tells BT Sport: "It feels amazing. You never take a win for granted. It was a weird game. The amount of work we put in during pre-season, to be in this position in Europe is a good stepping stone and a good reward.

"We’ve talked about defence since day one. That's our identity.

"No matter what the result is, we refresh on Monday and Tuesday and it all starts on our defence. People may think it’s about the flashy defence with Glasgow but it’s built on good defence which all good teams should be."

What jubliation for Glasgow. A first European final for the club beckons.

They were a bit scrappy in the second quarter, putting themselves under pressure, but barring that shaky 20-minute spell, they have bossed this contest.

Stafford McDowall book-ended the semi-final win with the first and last of the Warriors' five tries.

George Horne, Johnny Matthews and Rory Darge also crossed for Franco Smith's men.

Pack your bags, Warriors fans. You're off to Dublin for a shot at European glory.

We enter the final minute, and Glasgow win a penalty as George Horne is impeded at the breakdown.

Tom Jordan kicks down field, and finds a whopper of a touch right on the 5m line.

They can end this in style with another try.

Colin Gregor
Former Glasgow Warriors back on BBC Radio Scotland

George Horne too, with his place kicking and he scored a try - he's in with a shout for player of the match.

Peter Wright
Former Scotland prop on BBC Radio Scotland

Player of the match is probably Rory Darge. Zander Fagerson too.

You could probably argue Johnny Matthews for his second-half performance!

It's not happening for them.

A knock-on from Josh Macleod brings the attack to abrupt halt.

The home fans have fallen silent. Glasgow's travelling support are sounding the battle cry.

"We are Warriors!" rings around Parc y Scarlets.

Now it's Johnny Matthews whose line-out throw is a little skew-whiff.

Scarlets have a scrum, but they're some 70m from the Glasgow line.

It's now or never.

Glasgow dynamite the Scarlets scrum. Penalty Warriors.

This game is slipping away from the hosts.

Glasgow are four minutes from a European final.

Lewis Bean steals! What an introduction from the British Army rifleman.

Ali Price boots Glasgow clear. Shaun Evans throws in crooked.

Time ticking away for the Scarlets.