This year's winner will be announced in December, but all four nominated works will be on display until January.
In its four-star review, London's Evening Standard said: "The display of work by the four contenders efficiently captures art's current mood."
Mark Hudson in The Telegraph also gave the nominees four stars, but added: "Michelangelo it certainly isn't."
"There's plenty to exasperate the sceptic and give even the most receptive gallery-goer a headache," he added.
"None the less, this is one of the strongest Turner Prize shows in ages."
The Guardian's Adrian Searle said the show was "perhaps the most peculiar and baffling Turner prize show I can remember".
"I haven't enjoyed being so confounded and perplexed in a long time," he added.
But Rachel Campbell-Johnston from The Times gave the nominated works two stars, commenting: "This year's Turner display is nothing if not idiosyncratic."
She added the meaning of some of the artworks is not immediately clear when looking at them.
"You have to start with the written explanation and then work out how their objects illustrate their ideas.
"That's why I would like Helen Marten to win, she produces the most visually intriguing pieces of the four candidates."
The Guardian also tips "the inscrutable, endlessly inventive" Marten to win, saying she "makes life feel less bare, more rich, more absorbing".
The BBC's arts editor Will Gompertz said the same, adding that her artworks are "sort of time capsule stories containing an arrangement of clues that help the viewer solve a riddle".
The Turner Prize exhibition is at Tate Britain from 27 September until 8 January 2017.
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The fighter gave himself up when he was approached near the town of Sinjar on Monday morning, an Iraqi Kurdish general said.
He was reportedly carrying a large quantity of cash, three phones and a US driving licence.
The US is leading an international military coalition against IS.
The US state department said that it was aware of reports that a US citizen had been captured by Kurdish forces in northern Iraq, Reuters reports.
"We are in touch with Iraqi and Kurdish authorities to determine the veracity of these reports," a state department official said.
CBS News said the man was trying to enter Turkey when he was intercepted by Kurdish forces.
Maj Gen Feisal Helkani of the Kurdish peshmerga forces said the man was currently being held by the peshmerga for interrogation, AP reports.

The investors, Filmyard, includes construction magnate Ron Tutor and investment firm Colony Capital.
Disney has been negotiating with potential buyers for months to sell the division, which has made films such as Pulp Fiction and Shakespeare in Love.
Earlier this week, Disney bought the social gaming developer Playdom.
"Although we are very proud of Miramax's many accomplishments, our current strategy for Walt Disney Studios is to focus on the development of great motion pictures under the Disney, Pixar and Marvel brands," Disney's chief executive Robert Iger said.
Disney wants to concentrate on these family-orientated divisions, which produce popular films such as Toy Story, that also come with highly profitable merchandising opportunities.
"Disney has been very smart with its film strategy," media analyst Theresa Wise told BBC World Business Report.
"One of the big issues with movies is very few films break even... so they need other revenues. Disney has the fantastic ability to sell family films and all the merchandise that goes with it.
Disney has owned Miramax since 1993 when it bought the firm from Hollywood heavyweights Harvey and Bob Weinstein.
The Weinstein brothers, who recently attempted to buy it back from Disney, named the film company after their parents Miriam and Max.

The body of James Chadwick, 37, was found at an address in Holland Street last Wednesday.
At Aberdeen Sheriff Court, Ryan Gibb and Cameron Laurie, both 30, were charged with murder and attempting to defeat the ends of justice.
They made no plea and were remanded in custody. They are due to appear in court again next week.
Art critics have given broadly positive reviews to this year's Turner Prize exhibition at Tate Britain.
[NEXT_CONCEPT]
US officials are checking reports that an American member of the so-called "Islamic State" group (IS) has been held in northern Iraq.
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Entertainment giant Walt Disney has announced the sale of its Miramax film division for about $660m to a group of private equity investors.
[NEXT_CONCEPT]
Two men have appeared in court charged with the murder of a man in Aberdeen.