Best Actor Joaquin Phoenix and Best Actress Diane Kruger — Photos by AFP
Diane Kruger clinched best actress for her first film role in her native German as a devastated mother who has lost her husband and son in a neo-Nazi terror attack, in Fatih Akin's In the Fade.
"I cannot accept this award without thinking of everyone who has been touched by an act of terrorism... you have not been forgotten," said a visibly moved Kruger.
Chastain called it "disturbing" that there had not been more meaty female roles among the 19 contenders for the Palme d'Or. Only three of the films were made by women.
'So much courage'
Greece's Yorgos Lantimos shared best screenplay prize with Ramsay for The Killing of a Sacred Deer, an icy thriller set in a wealthy American suburb and also starring Kidman and Farrell.
The runner-up Grand Prix went to the hotly tipped French drama 120 Beats Per Minute about the radical activists who helped shame the world into action on AIDS.
"This film is an homage to those who died but also those who survived and are still alive, who had so much courage," said the movie's director, former ACT UP member Robin Campillo.
"I loved the movie. I couldn't love it more. I was touched since the very beginning until absolutely the end, and after the end," Almodovar said, fighting back tears.
Loveless by Andrey Zvyagintsev, a wrenching drama about moral rot gnawing at Russian society under Vladimir Putin, took the third place jury prize.
French daily Liberation called the picks "disappointing", having plumped for 120 Beats Per Minute, although Britain's Guardian hailed the selection as "a launching pad for a clutch of excellent films".
'Very funny'
The Square is an often savagely funny takedown of the limits of free speech and the blurred lines between the sexes.
Danish actor Claes Bang plays a museum director and divorced father of two young daughters who gets robbed in broad daylight in the city centre.
In the aftermath, he's forced to check his privilege and liberal political beliefs against a reality that seldom mirrors the rarified world of high culture.
The title refers to a conceptual art project in which museum visitors are invited to enter a "sanctuary of trust and caring", a tiny utopia in the middle of a flawed society.
The movie features Elisabeth Moss (Mad Men) and Dominic West (The Wire) in small roles viciously lampooning the self-important art world.
One set-piece, featuring a wild, bare-chested man performing as an ape wreaking havoc at a posh gala dinner, immediately entered Cannes legend.
Almodovar hailed the movie's themes as "completely contemporary".
"Such a serious subject is treated with such incredible imagination -- it's very funny," he said.
Ostlund defended the film's length at two hours and 20 minutes, saying that it was shorter than some Harry Potter sequels.
"If we want to make cinema walk tall again we have to put more complex questions into cinema," he said.