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.
Arsenal missed their chance to go back to the top of the Premier League after being forced to play with 10 men for much of the game against London rivals Chelsea on Sunday.
Manchester City took a major step towards retaining their Premier League title with a 1-0 win over second-placed Chelsea on Saturday, opening up a 13-point lead at the top of the table for Pep Guardiola's side.
News of all that's transpired on and off the football field
Adrian fired past opposite number and Spanish compatriot Joel Robles immediately after the Everton keeper had crashed his spot kick against the crossbar as West Ham won 9-8 on penalties.
As Chelsea's season suffered a final sorry implosion with an FA Cup defeat at Everton on Saturday, it was fitting that it should end with another display of fury from their angry young man, Diego Costa. While the inquest into the Premier League champions' dismal campaign will continue long after their 2-0 quarter-final reverse at Everton, the immediate topic consuming social media centred on the combustible Spain striker's sending-off, surprisingly his first for Chelsea. Alan Shearer, one of England's greatest strikers, joined the debate by telling BBC viewers the Brazilian-born forward had become "tiresome". Much of the attention focused on whether Costa, who became embroiled in a late face-to-face brouhaha with Everton's Gareth Barry, had gone as far as biting his opponent, Luis Suarez-style. Another question was whether he spat at the feet of referee Michael Oliver after being booked earlier for an altercation with Barry. "It's tiresome from him now. He spends too much time abusing and fighting and scrapping," Shearer said. "You can't do that every game because you turn the ref against you."
Photos from the English Premier League matches played on Wednesday
Manchester United manager Jose Mourinho said his French winger Anthony Martial is finally understanding exactly what is required from him after he delivered an outstanding performance in Sunday's 2-1 Premier League win over Everton.
On a seismic day in the history of Chelsea, Romelu Lukaku scored the winning goal in a 3-2 FA Cup fifth-round victory
An injury-time goal from Fulham's Darren Bent inflicted more pain on struggling Manchester United as the bottom club rescued a 2-2 Premier League draw on Sunday while Tottenham Hotspur beat top-four rivals Everton 1-0.
Chelsea striker Diego Costa needs to learn to show respect to opponents after the Spaniard goaded Everton players during their pulsating 6-3 English Premier League win on Saturday, Toffees coach Roberto Martinez said.
IMAGES from the English Premier League matches played on Saturday.
Romelu Lukaku scored two goals for Everton, one demonstrating rare strength and skill, to knock his old side Chelsea out of the FA Cup 2-0 in a dramatic quarter-final featuring two red cards on Saturday. All the frantic action happened in the final 13 minutes with Chelsea striker Diego Costa and Everton midfielder Gareth Barry sent off but their dismissals only came after Lukaku's brilliance had put the tie beyond doubt. The powerful Belgium striker, who never fitted in at Stamford Bridge and was sold to the Merseysiders for 28 million pounds ($40.28 million) two years ago, proved irresistible with his late five-minute double, especially with a first goal destined to go down in Goodison Park folklore. As the game meandered towards a replay, Lukaku conjured a 77th-minute goal from nowhere, muscling past two defenders on the left, powering into the box and, after some nifty footwork to bamboozle Gary Cahill, firing in a left-foot effort. Everton manager Roberto Martinez hailed it "one of the great goals we will see in the FA Cup".
IMAGES from the English Premier League matches played on Saturday.
IMAGES from Saturday's English Premier League matches.
A preview of the top matches coming up in the English Premier League.
English Premier League leaders Liverpool will need to maintain their excellent recent record against Everton in Sunday's Merseyside derby if they are to hold their advantage over second-placed Manchester City.
A preview of the line-up action in the English Premier League.
The injury to the Chile forward, who was left out of the squad for Tuesday's Champions League victory over Young Boys, "will require further investigation to confirm its severity", the club added.
A round-up off all transpired on and off the football pitch
Liverpool moved into the Champions League qualifying spots after a 3-0 win at Burnley on Wednesday took them above Leicester City and into fourth place with one round of Premier League matches remaining.
With Shkodran Mustafi also an injury doubt, manager Arsene Wenger is running out of central defensive options.
The club said in a statement that they will observe a period of self-isolation in accordance with league and UK Government protocols on quarantine.
Images from Premier League matches played on Wednesday.
Leaders Manchester City kept up their unbeaten run with a 3-1 win over Bournemouth on Saturday. Manchester United salvaged a 2-2 draw at Southampton, who sacked manager Mark Hughes on Monday.
With United unable to sign a replacement, the pressure will be on 21-year-old England forward Marcus Rashford to deliver the goals in a more central role than he has previously operated in.
Manchester City reached the League Cup final after recovering from a shaky start as Sergio Aguero's brilliant header sealed a 3-1 win over Everton in the semi-final second leg to clinch a 4-3 aggregate victory.
Harry Kane's 101st Premier League goal was the difference as Tottenham Hotspur earned a 1-0 win over Arsenal, to continue their fine recent form in north London derbies in front of a Premier League record crowd at Wembley on Saturday.
Tottenham Hotspur brutally exposed Liverpool's defensive frailties as Harry Kane plundered two more goals in his side's 4-1 romp at Wembley on Sunday.
In Pep Guardiola's 100th match in charge of the Manchester club, captain De Bruyne led from the front as City outclassed the Gunners, who have now suffered six home games without a win. Images from the EPL matches played on Sunday.
Jose Mourinho's side have been the most impressive of any of the title contenders.
High drama ensued during the English Premier League matches on Wednesday as Spurs manager Jose Mourinho was booked while Brighton stunned Chelsea via Alireza Jahanbakhsh's superb equaliser to deny the Blues victory. Here is all the EPL action in IMAGES from Wednesday's matches.
Images from Saturday's action in the Premier League.
Match-by-match facts and statistics ahead of the Premier League fixtures on April 28-30
Trippier suspension temporarily halted by FIFA
Champions Manchester United will travel to Swansea City for their first English Premier League match under new manager David Moyes, while Manuel Pellegrini's Manchester City are at home to Newcastle United on August 17.
Images from the English Premier League matches played on Saturday.
Zlatan Ibrahimovic's 28th goal of the season in all competitions put United ahead and Sunderland's cause became all but impossible after Seb Larsson was sent off close to halftime.
Officials were forced to call off the opening day of the first Test between England and the West Indies due to bad light and rain which saw only 17.4 overs being bowled.
News of all that's transpired on and off the football field