Image source, Getty Images

Back in the big time.

Liverpool join Chelsea, Tottenham, Manchester City, Manchester United and Celtic in the Champions League group stages.

Read Jonathan Jurejko's match report

We are back on Thursday for the draw and Europa League action.

Until then.

Champions League

Five English teams, one Scottish.

Draw takes place on Thursday from 17:00 BST.

Hoffenheim boss Julian Nagelsmann: "My thought (at 3-0 down) was this could be going better.

"We didn't start the match well at all. We had a game plan we didn't manage to implement."

Image source, .

Liverpool

More from Liverpool boss Jurgen Klopp: "We wanted a fast start and we have fulfilled our dream. It was fantastic.

"Playing Hoffenheim was the most difficult draw, alongside Napoli, we had two unbelievably hard games. We learned from the first game and adapted to a little change when they changed from five at the back to four at the back."

On tomorrow's group-stage draw: "We should be there and really excited about the group stage, whoever we get. There will be a few nice and difficult opponents but no-one with this atmosphere wants to get us. I'm really looking forward to the draw.

"Now I've told the boys to party. Enjoy it!"

On Coutinho: "There is nothing else to say. It's not that I don't want to talk about it, I just have nothing to say."

Liverpool

Liverpool manager Jurgen Klopp, speaking to BT Sport: "I do not have enough words it is amazing. It is 14 months of the hardest work and it feels amazing. I can't find another word.

"A big big big compliment to my team. They played a perfect opening half an hour. I asked them at half-time to remember the feeling they had at 3-0 and to put it away.

"But credit to Hoffenheim they played football and continued to enjoy the game. They can score two goals because of their quality.

"We didn't think we were the favourites but everyone else did so we had the pressure but the boys did good."

A beaming Jurgen Klopp says "the boys did outstandingly good" as "all the hard work of the past 14 months" came to fruition.

Full quotes to come from the Liverpool manager.

• Liverpool have returned to the Champions League group stages for the first time since the 2014-15 campaign.
• Liverpool have scored 3+ goals in consecutive European home games (including qualifiers) for the first time since March 1997.
• The Reds have now won six successive European games at Anfield (including qualifiers) against German opposition.
• Jurgen Klopp has overseen seven European games (including qualifiers) as Liverpool manager at Anfield, with the Reds winning each of the last six; their best run since November 2010 (eight successive wins).

• Emre Can has scored 2+ goals in a game for the first time in his professional career.
• Sadio Mane has been directly involved in 15 goals in his 17 appearances at Anfield for Liverpool (10 goals, 5 assists).

Liverpool

Liverpool captain Jordan Henderson, speaking to BT Sport: "It has been a brilliant night, the atmosphere was brilliant all night and we were brilliant at the start and set the tempo.

"We let in a couple of goals so we have still got things to work on but overall we're delighted to get back into the Champions League where Liverpool belong.

"Getting back in to the Champions League was our aim and we've done it. Now when we get into the Champions League itself we have got to do ourselves justice and win some games there.

"I'm delighted for the lads and the fans. We're in there and we've proved we can play against big teams. We're happy to play against whoever we're drawn against."

Mandeep Sanghera
BBC Sport at Anfield

Emre Can gets a bear hug off Jurgen Klopp as the Liverpool bench celebrate at the final whistle. Mo Salah also gets one before Klopp applauds the Kop to huge roars and beats his chest on the way off.

Now for the draw on Thursday.

Liverpoool boss Jurgen Klopp runs on to the pitch and shakes the hands of each of his players.

He them punches the air in delight in front of the Kop End.

Loving it.

"The Cham-pions," tu tu-tu tu tuuuuu.

Job done, Champions League football is back at Anfield.

Jurgen Klopp with a smile from ear to ear.

Liverpool left-back Alberto Moreno is the furthest man forward for the hosts in injury-time.

Hah.

Late corner for Hoffenheim.

Cleared.

Benjamin Hubner booked late on. He's not happy.

A tremendous round of applause for man-of-the-match Sadio Mane, who makes way for Ragnar Klavan.

With Mane on form like this, Liverpool should take the £138m for Coutinho and run.

Goallll.

Ah, sorry, side netting.

Roberto Firmino smashes a drive narrowly wide of goal.

Mandeep Sanghera
BBC Sport at Anfield

To be fair, Hoffenheim's fans are banging out plenty of chants in support of their team. I haven't got a clue what they're singing but one of the songs is to the tune of 'I love you baby'. Catchy.

Five minutes remaining to see if we have any more goals.

We've had six already, am I being a bit too greedy there?

Alberto Moreno trots forward unchallenged and gives a souvenir to a fan in the Kop with a wild strike.

Shane Daly: Liverpool fans please calm down, the group stages is where the big boys play, we will see how good you are then.