Smith has been in charge since 1998 at Goodison Park, but has never taken Everton above 13th in the table during his time at the club.
Fact File
Managers leaving this season
Peter Taylor - Leicester
Jim Smith - Derby
Stuart Gray - Southampton
Colin Todd - Derby
John Gregory - Villa
Walter Smith - Everton
Some people have said one of the reasons Smith has struggled is because he hasn't been given enough money to spend on players.
He has spent £57.8m during his reign, but he has had to raise that money himself, selling £57.15m of players.
David Moyes could be the new boss
Before he went to Everton Smith managed Rangers, and took them to 13 trophies in his seven years in charge, but he wasn't able to transfer that success to the Premiership.
The person most likely to take over seems to be Preston North End boss David Moyes, who took the club to the division one play offs last season, and is hotly tipped to become a very successful manager in the future.
Hear story
Chat about football
World Cup 2002 quiz
