With Crystal Palace dangerously close to being relegated, manager Patrick Vieira was sacked after 20 months in charge.
Liverpool manager Juergen Klopp said that his side should be awarded the three points if Monday's game against Manchester United at Old Trafford is called off due to home fans protesting against their owners.
Liverpool and Manchester City having the potential to "dominate" European football, former Scotland international Graeme Souness has said.
Images from Saturday's action in the Premier League.
Chelsea, who won the Champions League last season, begin their season at home to Crystal Palace before trips to Arsenal and Liverpool.
Images from Sunday's action in the Premier League
Arsenal's bench celebrated Monday's 1-0 win at Crystal Palace as if it was the Premier League title decider despite only being the second week of the season.
Chelsea will look to make amends after being runners-up to Leicester City and Arsenal in the last two seasons
IMAGES from the Premier League matches played on Sunday.
Images from the English Premier League matches played on Sunday night.
Images from the football matches played on Tuesday.
Manchester United's miserable season continued with a 3-2 home defeat by Galatasaray.
Arsenal, who finished fifth last season, brought in Jesus and Zinchenko from Manchester City for a combined 75 million pounds ($91.04 million).
IMAGES from the English Premier League matches played on Saturday.
Leaders Manchester City were held to a 0-0 draw at Crystal Palace
It was a third successive 0-0 draw for United after a stalemate at Chelsea on Sunday and against Real Sociedad last Thursday which completed a 4-0 aggregate win over the Spanish side in the Europa League.
Images from Saturday's action in the Premier League.
Liverpool will resume their quest for a first top-flight title in 30 years at city rivals Everton on June 21, as the English Premier League released its revised fixture list for the first three weeks of the restarted season on Friday. Liverpool are 25 points clear at the top and are two victories away from winning the Premier League, but will have a shot at securing the title by beating Everton if City lose to Arsenal.
Images from Sunday's action in the Premier League.
Holders Liverpool survived a penalty shootout to see off third-tier Derby County
The 22-year-old has signed on an eight-and-a-half-year contract in deal worth 100 million euros ($108 million).
Liverpool snatched three points with a wild 1-0 victory over relegation-threatened Nottingham Forest.
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.
Kane headed home from Christian Eriksen's corner in the 89th minute to make up for two glaring misses earlier in the match at Selhurst Park.
Wolves midfielder Leander Dendoncker then hit the post with a powerful shot before Portuguese winger Podence made it 2-0, meeting Pedro Neto's cross from the right with a superb cushioned volley in the 27th minute.
Leeds sack Gracia, Allardyce to step in till season ends
'United can change nothing or everything, so it's tricky preparation-wise, but it's early and we don't have a lot of info. It's tough... United away will never be easy.' Liverpool manager Juergen Klopp says wounded Man Utd will not be easy to play.
West Ham United midfielder Cheikhou Kouyate is free to face Arsenal on Saturday after the Football Association rescinded the red card he received against CrystalPalace in last weekend's 2-2 Premier League draw.
Liverpool forward Sadio Mane scored his 100th goal for the club to help secure a 3-0 victory over lively Crystal Palace in the Premier League at Anfield on Saturday.
Gerrard's side turned their fortunes around at the expense of the visitors under Lampard
Harry Kane said his World Cup penalty miss that condemned England to a quarter-final exit will stay with him for the rest of his life.
As the highly-anticipated derby got underway, Brighton allege that a small number of Palace supporters showed up without tickets and tried to force their way into the away end of the stadium.
Curtin Jones's 71st-minute strike saw Liverpool edge past Everton in a derby tie at Anfield.
Images from Tuesday's action in the Premier League
Images from the English Premier League matches played on Saturday
Images from Saturday's action in the English Premier League
Everton striker Romelu Lukaku struck a late equaliser to salvage a 1-1 draw against a solid CrystalPalace side in an absorbing Premier League match at Goodison Park on Monday.
IMAGES from the English Premier League matches played on Saturday.
It is a first win in six games in all competitions for Liverpool.
Images from the English Premier League match played between Arsenal and Crystal Palace on Monday