Goals from Ragnar Sigurdsson and Kolbeinn Sigthorsson cancelled out Wayne Rooney's early penalty, as the outsiders' remarkable debut at a major tournament continued with a 2-1 success.
Iceland will now take on hosts France in the quarter-finals in Paris on Sunday, while England are left to contemplate another ignominious exit.
With Hodgson resigning after four years at the helm, we look at five possible contenders to take charge.
The England Under-21 boss appears the man in pole position to take over. He is well established at the Football Association, although he endured a mixed record as manager of Middlesbrough and his Under-21 side finished bottom of their group at the European Championship last year.
Along with fellow assistant Ray Lewington, the former Manchester United defender also departed following the Euro 2016 exit. Neville suffered a torrid time in charge of Valencia last season, but is well respected in the game and his passion was clear for all to see following Daniel Sturridge's dramatic winner against Wales in the group stage.
Looked a strong candidate after a stellar first half of 2015-16 in charge of Crystal Palace. But their form after Christmas tailed off badly as they briefly became embroiled in the relegation scrap before pulling away. His case is helped by Palace's FA Cup final appearance, where they lost out to Manchester United.
Worked minor miracles at AFC Bournemouth, guiding the club away from the foot of League Two and possible extinction to the Premier League, either side of a brief spell at Burnley. His ability to keep Bournemouth in the top flight with seeming ease last season proves his credentials, although at just 38 this vacancy may have come too early for him.
Originally considered for the post following Sven-Goran Eriksson's departure after the 2006 World Cup, only to miss out to Steve McClaren. Did a commendable job in keeping Sunderland in the Premier League last season, and has forged a reputation as a solid operator in the top flight, although his style of football has occasionally been questioned.