Postpublished at 22:32 Greenwich Mean Time 5 March
That's all from us tonight. I'll leave you with the reports from both games and join us again tomorrow night when Manchester City are in action.
FT: Bayern Munich 3-0 Lazio (agg 3-1) - Kane scores twice as Bayern come back to win tie
FT: Real Sociedad 1-2 PSG (agg 1-4) - Mbappe double helps visitors through
Man City play Copenhagen on Wednesday, Arsenal face Porto on 12 March
Draw for quarter-finals and semi-finals takes place on 15 March
Gary Rose and Tom Rostance
That's all from us tonight. I'll leave you with the reports from both games and join us again tomorrow night when Manchester City are in action.
FT: Bayern Munich 3-0 Lazio (3-1 agg.)
Archie Rhind-Tutt
German football journalist on BBC Radio 5 live
To go and score twice tonight is a step for Harry Kane. But here at Bayern you are judged on the biggest nights when you come face to face with Europe's elite.
It was clear tonight that that is not a level that Lazio are in, it is a good night for Harry Kane, but it will be viewed as, "There are bigger challenges to come."
FT: Bayern Munich 3-0 Lazio (3-1 agg)
Bayern Munich striker Harry Kane, speaking to CBS: “It was an important night tonight.
"It can really change the momentum of the season.”
FT: Real Sociedad 1-2 Paris St-Germain (Agg 1-4)
Glenn Hoddle
Former England and Tottenham manager on TNT Sports
You are thinking how is he going to score from there [for the first goal]? But he shifts it so quickly before you know it the ball is in the back of the net. The defender goes for an ice cream. When he is that form he is unplayable.
FT: Bayern Munich 3-0 Lazio (3-1 agg.)
James Horncastle
European football writer on BBC Radio 5 Live
The outcome of this tie is expected, regardless of what Bayern have been going through in this past month. Maurizio Sarri didn't expect to go through, he said as much in his press conferences before each leg of the tie.
I suppose the regret now if you look back is that Lazio played the final 20 minutes of that first leg against 10 men. Ok they didn't expect to be 1-0 up in that game, but could they have capitalised more then?
In this second game, before Bayern took the lead, Ciro Immobile had a header at the far post. For a player of his experience, who has been prolific in the Champions League for two clubs, that was disappointing.
If they found themselves 2-0 on aggregate at that stage it would have been very interesting.
FT: Bayern Munich 3-0 Lazio (3-1 agg.)
Pat Nevin
Former Chelsea and Scotland winger on BBC Radio 5 Live
There is still something missing from Bayern.
In the past we looked at Bayern as real contenders for the Champions League. In reality, if you put Man City in front of them tonight, both playing their best sides, City would wipe the floor with them. Absolutely wipe the floor with them, all over the pitch.
But that is not necessarily how it plays out in reality because City will be battling and chasing in the Premier League and the FA Cup. The only thing that you think will stop City in the Champions League is that they will be stretched far more than anyone else left in the competition.
FT: Real Sociedad 1-2 Paris St-Germain (Agg 1-4)
Paris St-Germain striker Kylian Mbappe: "We knew right away that we couldn’t go to sleep. If they had opened the scoring, they would have pushed on with their fans’ backing. We had to dampen their hopes early on. That’s what we did, and we’re very happy to be back in the quarter-finals.”
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I think people are getting a bit hyperbolic about Bayern. They beat 9th place Lazio, at home. Brighton are 9th in a better league and I don't think anyone would be surprised if Bayern beat them 3-0. I'll bet my lederhosen the Bavarians go out in the next round.
Franz, Munich
FT: Bayern Munich 3-0 Lazio (3-1 agg)
Harry Kane has now scored 27 Champions League goals, with Wayne Rooney (30) the only Englishman to score more in the competition.
He also has more combined goals and assists in this season’s competition than any other player (9 – 6 goals, 3 assists).
FT: Bayern Munich 3-0 Lazio (3-1 agg.)
Pat Nevin
Former Chelsea and Scotland winger on BBC Radio 5 Live
Before Bayern scored the first goal through Harry Kane, I wouldn't go as far to say they looked nervous, but they weren't ultra confident. Now after the second goal, that completely changed.
I've watched that happen so many times to Bayern over the years. A bit of edginess before they go ahead, and then once they're ahead they are really comfortable, it looks easy and they are pulling tricks off.
Most teams are like that, however the good teams believe in themselves and have the confidence throughout before the goals go in.
Bayern Munich 3-0 Lazio (3-1 agg)
Owen Hargreaves
Former England midfielder on TNT Sports
Bayern are still one of the best sides in the Champions League, maybe the problem is the depth when people are missing.
Bayern Munich 3-0 Lazio (3-1 agg)
Rio Ferdinand
Former England defender on TNT Sports
This is the true mark of a great goal scorer, they don't have to be in the game all the time, they have to be in the right place at the right time.
This is what Harry Kane has done all his career and that's why he has scored so many goals.
Not long for Bayern and PSG to wait to find out who they face next - The quarter-final, semi-final and final draws take place in Switzerland, on Friday 15 March.
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The young lad Pavlovic was the best player on the pitch tonight; he looks like a real prospect
James, West Ham fan
FT: Real Sociedad 1-2 Paris St-Germain (Agg 1-4)
John Bennett
BBC Sport
The transfer saga has too often overshadowed how wonderful it is to watch Kylian Mbappe in full flow like he was tonight.
FT: Bayern Munich 3-0 Lazio (3-1 agg.)
Pat Nevin
Former Chelsea and Scotland winger on BBC Radio 5 Live
If anyone has any injury worries now, any little niggles between now and the rest of the games in this competition, Thomas Tuchel will rest them. Harry Kane? Manuel Neuer? No risks, just rest them.
There is nothing they can do realistically about the league, they are out of the cup, so they will throw everything they can into the Champions League now.
FT: Real Sociedad 1-2 Paris St-Germain (Agg 1-4)
PSG are into the last eight after a night of minimal fuss. Kylian Mbappe is still there and that means they still have a chance. In any game.
Bayern Munich 3-0 Lazio (3-1 agg)
All over and Bayern Munich cruise into the quarter-finals thanks to a Harry Kane double and a Thomas Muller goal.
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How far will PSG & Bayern go? Last 8 looks like them with Real, Man City, Arsenal, Barca, Inter & Dortmund. These two aren't the heavyweights in that company!
Paul
Mikel Merino (89 mins)
Or we could stay here for another 30 seconds and they will score!
Gigi Donnarumma does well to claw out a driven cross from the right but former Newcastle man Mikel Merino is well placed to smash in the bouncing ball past a defender on the line and in.