Postpublished at 19:31 British Summer Time 25 June 2016
It's a shame to say goodbye to Northern Ireland, but Wales' journey is proving to be fantastic story.
Next up is Belgium or Hungary on Friday. Can they keep the fairytale going?
NI defender McAuley poked Bale's cross past own keeper
Wales' Ramsey had a goal disallowed in 19th minute
Wales will play Belgium or Hungary in quarter-finals
Gary Rose
It's a shame to say goodbye to Northern Ireland, but Wales' journey is proving to be fantastic story.
Next up is Belgium or Hungary on Friday. Can they keep the fairytale going?
Almost time for us to bring our coverage to a close but before we do, may I point you in the direction of the final last 16 game of the day - Croatia versus Portugal. Follow the action here.
Wales 1-0 Northern Ireland
Northern Ireland manager Michael O'Neill: "It's devastating. We were the better team on the day.... the nature of that goal. I couldn't ask anything more of the players throughout the tournament. Gareth McAuley knows he has to make one of those decisions on the cross - he had to judge whether there was someone behind him or not."
Wales 1-0 Northern Ireland
Chris Coleman
Wales manager on BBC One
It's amazing. First and foremost commiserations to Northern Ireland. We showed a lot of heart and courage. The good thing about these boys when we're not playing well is that they have spirit. And at times we were hanging on. I'd rather be standing here in the quarter-final not playing at our best. We have to give credit to Northern Ireland - they made it very difficult to play against. They were the better team. We have to plan for the next game whoever it is. We'll enjoy this tonight.
Richard Matthews: 20 mins since the full time whistle and the NIR fans are still cheering loud for their side inside the stadium!
Wales and Northern Ireland fans are still inside the stadium singing songs about Will Grigg. Does he only exist in song form?
I'm starting to think Will Grigg the player is a myth.
Wales 1-0 Northern Ireland
Wales' Gareth Bale on BBC One: "What can I say? We knew it was going to be an ugly match. Northern Ireland made it difficult to play - there was not much space up front. It's incredible."
Wales 1-0 Northern Ireland
Gerry Taggart
Former Northern Ireland on BBC Radio 5 live
I can't fault the effort of the players, Michael O'Neill got his tactics spot on again but we had a lack of cutting edge up front. That is the only disappointment.
We were the better team, we stopped Wales doing what they do best and we saw more balls in the second half.
Gareth Bale got into the game more when he pulled to the left and the ball into the corridor of uncertainty was a fantastic pass, leading to Gareth McAuley sticking it into his own net.
What a spectacle for British football.
Wales 1-0 Northern Ireland
Here's a stat Wales fans may like.
Wales are the first team to win a match in the knockout stages of the Euros with just one shot on target since Greece in the 2004 final.
Could this be the year of the underdog once again?
Wales 1-0 Northern Ireland
Dean Saunders
Former Wales striker on BBC One
The whole result is so important for Welsh football. Gareth Bale is the person they look up to.
Wales 1-0 Northern Ireland
Wales 1-0 Northern Ireland
Sarah Morgan: Well done Wales on quarter final place but well done Northern Ireland, too for showing such determined passion. Will miss you!
Belle: You beauty #Wales, external#bbcEuro2016, external not pretty but it's the result that counts!
Jmac: Bad luck #NIR, external a step too far but brilliant tourney. Good luck to #WAL, external believe in yourselves and you CAN win this
Wales 1-0 Northern Ireland
John Hartson
Ex-Wales striker on BBC Radio 5 live
Wales edged it. The two second half substitutions of Jonny Williams and Hal Robson-Kanu gave us some fresh impetus and an outlet.
Northern Ireland started the second half the better team, it took a deflected own goal to separate the two teams. Northern Ireland gave everything.
Wales 1-0 Northern Ireland
Wales' prize for progressing? It will be either Hungary or Belgium in Lille next Friday for a place in the semi-finals.
What a tournament they are having!
Wales 1-0 Northern Ireland
Robbie Savage
Ex-Wales midfielder on BBC One
It was a magnificent tournament for Northern Ireland. One quality delivery from a world class player was the difference between the two sides.
Wales 1-0 Northern Ireland
Unfortunate for Northern Ireland. They gave as much as they could and certainly had their chances.
In the end, though, it was Gareth Bale who made the difference. His superb cross forcing Gareth McAuley to turn home.
Wales 1-0 Northern Ireland
All over! WALES ARE INTO THE QUARTER-FINALS.
Wales 1-0 Northern Ireland
...Northern Ireland win a corner, the keeper is up! But Wales clear!
Surely that's it?