That's enough from me. Congratulations to Celtic on a job well done. Tougher tests await.
St Johnstone, Motherwell and Aberdeen are all in Europa League action on Thursday. Can they follow Celtic's lead and make progress?
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BBC Scotland's Tom English on Twitter: "Attendance estimate 36,000. Not had exact figure yet."
Celtic will be back at Murrayfield for the home leg of the third round qualifier since it will take time to get Celtic Park back to normal after the opening ceremony of the Commonwealth Games.
More from Celtic boss Ronny Deila
"We need to invest but it needs to be the right players. We will do it our way, like the club has always done. We are working hard on that."
Celtic manager Ronny Deila on BBC Radio Scotland
"The first half was good, we started well. We created good chances and won the ball back quickly to keep up the pressure. It was a bit sloppy at times in the second half but I have to be happy with the result.
"It's a good start but this is not the best opponent we are going to get."
Former Scotland striker Billy Dodds on BBC Radio Scotland
"Another creative player and a striker, that'll do nicely for the Celtic fans."
Fraser Forster wasn't troubled at all tonight. With Southampton sniffing around, can Celtic afford to sell their goalkeeper? He'll be a tough man to replace but if Craig Gordon can rediscover his form of old then maybe it would make sense.
Lukasz Zaluska was on the bench tonight, which might suggest Gordon is not quite there yet after his lengthy lay-off.
Tom English on BBC Radio Scotland
"I'm a huge Kris Commons fan but there is too much onus on him and I still think Celtic need a poacher up front. It's now a question of ambition. Will they go out and spend the money to make sure of Champions League football? But it's not a new question, Celtic fans have been asking it for a while and I suspect they know the answer."
Next up for Celtic is either St Patrick's Athletic or Legia Warsaw. That tie is poised at 1-1 ahead of tomorrow's second leg in Dublin.
Celtic 4-0 KR Reykjavik (5-0)
Two goals apiece for Virgil van Dijk and Teemu Pukki on a comfortable evening for Celtic. Two more rounds to negotiate if there is to be Champions League group stage football for a third consecutive season.
Former Celtic defender Mark Wilson on BBC Radio Scotland
"It's been a thoroughly professional job from Celtic. They came out of the traps quickly and killed the tie off."
Charlie Mulgrew, captaining Celtic in the absence of the injured Scott Brown, takes aim from 25 yards and Magnusson is right behind it.
We're into the last few minutes at Murrayfield and the referee is surely going to put KR out of their misery by not adding much in the way of stoppage time.
HITS THE WOODWORK
Here he comes again and this time the post denies Kris Commons as he meets a low cross with a first-time strike. Time is running out for the playmaker to get on the scoresheet.
It's a bicycle kick from the lively Kris Commons now and it flies high over the crossbar...
As I was sorting out that picture of Teemu Pukki's fine finish, Kris Commons had a go with a dig from fully 40 yards but his shot drifts over.
Here's Teemu Pukki hammering in the fourth goal for Celtic and yes that's the KR goalie behind him after a rash adventure into no man's land. It's not been a great night for Mr Magnusson.
Callum McGregor wants to get in on the scoring act after his debut goal last week but his lofted effort is gathered comfortably by Magnusson.
Teemu Pukki gets a huge roar of approval as he trots off to be replaced by Liam Henderson.
Celtic 4-0 KR Reykjavik (Pukki)
It's two goals for Teemu Pukki, who bursts past the stranded goalie on the edge of the box, beats a defender, then thrashes the ball home from a tight angle.
Mikael Lustig gets forward menacingly, with Callum McGregor creating space for the full-back. The Swedish defender drills in a cross, which has goalie Magnusson in trouble, but there are no takers in green and white.