Manchester City and Manchester United have already booked their places in next season's Champions League, but two spots are still up for grabs in the Premier League and it could go right down to the wire.
Who qualifies for Europe?
Champions League: 1, 2, 3, 4
Europa League: 5, 6
Europa Conference League: 7
If an English team wins one of the European trophies, there can be no additional places.
Here's what the teams need to do to qualify for the Champions League, and the other European places.
Victory over Leicester on Tuesday means Chelsea have a place in next season's Champions League in their own hands. Win at Aston Villa on Sunday and it's job done. If they don't win but match or better the result of either Leicester or Liverpool, they will also qualify.
Draw against Villa and Chelsea will qualify as long as both Leicester and Liverpool don't win.
With a defeat at Villa Park, Chelsea can still be in the top four as long as either Liverpool lose to Palace or Leicester lose or draw against Tottenham. If Liverpool draw with Palace and Leicester beat Spurs, then Chelsea will finish fourth.
If Chelsea do end up outside the top four, they will have to beat Manchester City in this year's final in Porto on May 29 to book a return.
Liverpool's fate isn't technically in their own hands, as they could still finish behind Leicester on goals scored or goal difference. But the 3-0 victory at Burnley means a win at home to Palace will almost certainly book a Champions League spot.
If both Liverpool and Leicester win, then the Foxes must win by four more goals. So if Liverpool win 1-0 against Palace, Leicester must win 5-0 to go above them. Of course, if Chelsea fail to win then victories for both Liverpool and Leicester send both through regardless.
A draw would also be enough as long as Leicester don't win, and if both teams lose the goal difference means Liverpool would need to lose at least 5-0 to miss out.
5. Leicester (37 games, 66 points)
Remaining game: Tottenham (h)
Although Leicester can still climb back into the top four if they thrash Spurs (with Liverpool and Chelsea winning), it's highly likely they must better Liverpool's result OR win with Chelsea drawing or losing. Nothing else will work for them if they are to avoid the Europa League.
6. West Ham (37 games, 62 points)
Remaining game: Southampton (h)
West Ham are very much in pole position for a place in the Europa League. A point at home to Southampton will secure it.
Goal difference means the only realistic way they can miss out is if they lose and Spurs win at Leicester.
Although Everton are also three points behind, their goal difference is eight worse. It means the Hammers should at the very least have UEFA Europa Conference League football.
7. Tottenham (37 games, 59 points)
Remaining game: Leicester (a)
Spurs' main aim now is to try and overhaul West Ham. They have to beat Leicester and hope West Ham lose at home to Southampton.
If they don't win at Leicester they may well miss out on Europe altogether.
8. Everton (37 games, 59 points)
Remaining game: Man City (a)
Everton's poor goal difference means their only realistic hope is seventh and the UEFA Europa Conference League. But they have to play Man City away.
If Everton win at the Etihad, they have to hope Spurs do not beat Leicester.
If Everton draw at City, they must hope Spurs lose and Arsenal fail to win.
They cannot realistically qualify with a defeat.
9. Arsenal (37 games, 58 points)
Remaining game: Brighton (h)
Goal difference means Arsenal must win at home to Brighton and hope neither Tottenham or Everton win to secure European football against the odds.
10. Leeds (37 games, 56 points)
Remaining game: West Brom (h)
Leeds only have a mathematical chance with one game remaining, as they are three points and 15 goals worse off than Tottenham in 7th.