City forward Erling Haaland, who had missed a first-half penalty, made amends in the 57th minute
Real Madrid beat holders Manchester City in an edge-of-your-seat 4-3 shootout victory to reach the semi-finals of the Champions League.
Barcelona won 3-1 at Alaves in La Liga on Saturday thanks to goals by Robert Lewandowski, Ilkay Gundogan and substitute Victor Roque, who was sent off after picking up a second yellow card.
Images from the Champions League Round of 16 matches.
Chelsea manager Graham Potter and his family have received anonymous death threats following the English Premier League club's poor run of results.
Bayern Munich striker Harry Kane arrived in Germany on a record-breaking transfer and his sensational goal-scoring run this season has already exceeded expectations and turned him into an instant fan favourite.
Images from the football matches played on Tuesday.
Record-breaking Kane scores hat-trick in Bayern's 7-0 demolition of Bochum
Images from the Premier League matches played on Sunday.
New Chelsea manager Mauricio Pochettino underlined the challenges that engulfed Enzo Fernandez, Mykhailo Mudryk and Raheem Sterling in the last season but said he will help the trio.
Bayern Munich's Polish striker Robert Lewandowski won the FIFA Best Men's Player award for 2021 with Barcelona's Spanish midfielder Alexia Putellas winning the FIFA Best Women's Player prize at Monday's ceremony.
Athletic Bilbao beat Barcelona 4-2 at home to knock them out of the Copa del Rey
Harry Kane scored twice in his first league appearance in front of a home crowd to steer champions Bayern Munich to a 3-1 victory over Augsburg.
In a thriller at Anfield, a weakened Liverpool side came back from the brink to beat Leicester City on penalties after a 3-3 draw, setting up a semi-final against Arsenal.
League Two (fourth tier) side Stevenage pulled off the shock of the weekend by winning 2-1 at Premier League Aston Villa.
City need three points to be sure of securing their third title in four years
PSG's Neymar out until at least mid-November says Tuchel
Erling Haaland set another scoring record as Manchester City beat Bayern Munich
IMAGES from the English Premier League matches played on Sunday
Chelsea won their first competitive match under coach Mauricio Pochettino with a 3-0 home victory over Premier League new boys Luton Town.
Romelu Lukaku scored for Chelsea in a 5-1 FA Cup third-round victory
The Englishman lasted 31 games, winning only 12, before the owners pulled the trigger.
If Aubameyang's transfer to Chelsea goes through, he would return to the English top flight after seven months, having played for Chelsea's London rivals Arsenal for four years.
Liverpool's Mohamed Salah ended his Premier League goal drought in style by scoring twice as the champions raided the capital again to crush West Ham United 3-1 on Sunday.
Jorginho's first-half penalty earned Chelsea a 1-0 victory over Tottenham Hotspur in the Premier League on Thursday.
Chelsea will look to make amends after being runners-up to Leicester City and Arsenal in the last two seasons
The three Premier League and three La Liga clubs in the last eight avoided each other, with Manchester City up against Atletico Madrid and Liverpool to face Portuguese side Benfica.
Chelsea remain in fourth place, and are two points off third-placed Leicester City who have a game in hand.
Manchester City face Chelsea in the Champions League final on Saturday. Here are five key tactical battles to watch out for:
Chelsea slipped up in their push for a Champions League spot when they lost 1-0 at home to Arsenal in the Premier League on Wednesday with Emile Smith Rowe's first-half goal settling the London derby after a defensive mix-up by the hosts.
All the action that transpired on and off the football field
A summary of the concluding day's action in the Bundesliga, Serie A, Ligue 1 and Saudi Pro League.
Liverpool held their nerve to win an astonishing penalty shoot-out 11-10 and edge out Chelsea in the English League Cup final on Sunday after a rip-roaring contest had somehow ended 0-0 after extra time at Wembley.
Paris St Germain believe they can learn from their run to the Champions League final and become European champions after coming closer than ever in Sunday's 1-0 loss to Bayern Munich.
The Brazilian is likely to make his first appearance of the season for the Ligue 1 leaders at home against Racing Strasbourg on Saturday.
Thirteen-times European champions Real, who had come through each of their last three Champions League semi-final ties, had been second best for much last week's first leg which ended 1-1.
Updates from around the different clubs in the English Premier League
Chelsea beat Sheffield United 2-0 to reach the FA Cup semi-finals for the fourth time in five seasons.
Havertz's late penalty seals world club crown for The Blues
Chelsea won their second Champions League title and denied Pep Guardiola's Manchester City their first with Kai Havertz grabbing a first-half goal to secure a 1-0 win in Saturday's all-English final at the Estadio Do Dragao in Porto.