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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Art critics have given broadly positive reviews to this year's Turner Prize exhibition at Tate Britain.