Premier League champions Chelsea eased past a disappointing Everton with goals from Spaniards Cesc Fabregas and Alvaro Morata sealing a 2-0 victory on Sunday.
Manchester United survived a tense finale to beat West Bromwich Albion 2-1 at the Hawthorns on Sunday and close to within 11 points of Premier League leaders Manchester City.
Wayne Rooney scored two first half goals to help send Manchester United to a 4-1 win over a spirited Aston Villa on Saturday, temporarily lifting the gloom surrounding David Moyes' dismal first term in charge.
Lionel Messi, Luis Suarez and Neymar were all on target as holders Barcelona beat Athletic Bilbao 3-1 on Wednesday to overturn a deficit from the first leg and advance to the quarter-finals of the King's Cup.
Images from the English Premier League matches played on Saturday.
Second-half goals from Leroy Sane and Raheem Sterling stunned Arsenal at the Etihad Stadium on Sunday as Manchester City came from behind to win 2-1 and move seven points behind leaders Chelsea.
Diego Costa was on target again as Chelsea overcame a defensive West Bromwich Albion 1-0 to return to the top of the Premier League with their ninth victory in a row on Sunday. The Spaniard's second-half strike sent the Blues three points clear of Arsenal, who had taken the overall lead on goals scored on Saturday after seeing off Stoke City 3-1 at the Emirates.
Gabriel Jesus came off the bench to secure Manchester City a 1-0 English Premier League victory at Leicester City after yet another penalty miss by Pep Guardiola's side on Saturday. Chelsea's Olivier Giroud and Marcos Alonso returned to the starting lineup to stunning effect by grabbing a goal apiece in a crucial 2-1 home win over Tottenham Hotspur in the battle between the London rivals for fourth place.
Images from the English Premier League matches played on Saturday
Liverpool flirted with what would have been an embarrassing low in their poor start to the season as they were taken to penalties by fourth tier Carlisle United, but came through to reach the League Cup fourth round on Wednesday.
IMAGES from the English Premier League matches played on Wednesday.
Images from the English Premier League matches played on Saturday
Swansea City came from behind to end Manchester United's unbeaten start to the Premier League season with an impressive 2-1 victory at the Liberty Stadium on Sunday.
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Substitute Jesse Lingard struck twice in the second half as Manchester United fought back from 2-0 down to earn a 2-2 Premier League draw with Burnley at Old Trafford on Tuesday.
Mohamed Salah struck four times in rampant Liverpool's 5-0 thrashing of Watford that lifted them back into third spot in the Premier League on Saturday.
Raheem Sterling scored a hat-trick as champions Manchester City made a convincing start to their title defence with a 5-0 win over West Ham United.
Swansea City's hopes of salvaging their place in the Premier League suffered a potentially grievous blow as Ryan Fraser's deflected strike earned Bournemouth a 1-0 win on Saturday to secure another season of top-flight football for the Cherries.
Liverpool had won each of their previous four home leagues games in which they conceded first and 12 minutes later they had turned another match on its head as Roberto Firmino's trickery set up Mane to give the hosts the lead at the second attempt.
Arsenal maintained their challenge for a first trophy in nine seasons when they beat Liverpool 2-0 at the Emirates Stadium to open up a five-point lead at the top of the Premier League on Saturday.
A summary of the results of the major European football league matches on the weekend.