Whether outraging the conservative arts establishment by defacing etchings of Goya or appalling the general public with child mannequins sprouting genitalia from all the wrong places, they have soaked up influences from the Spanish painter Goya to the wilder edges of Surrealism to spit out a rude and scabrous art that constantly grabs headlines.
Last month, the brothers opened a mid-career retrospective at Tate Liverpool, entitled Bad Art for Bad People. It was packed with nearly all of their most famous works with the notable exception of Hell, the giant tableaux of murderous Nazis which was - terribly, but perhaps not inappropriately - destroyed in the Momart warehouse fire of 2004.
And today Tate Britain joins in the Chapman brothers celebration with the unveiling of a major new work - albeit one modelled on an earlier sculpture already in the gallery's collection.
When Humans Walked the Earth takes elements of the 1993 piece Little Death Machine (Castrated) - including a brain, milk bottles and tools - and reproduces them in bronze to create a series of impossible Heath Robinson-esque machines.
Clarrie Wallis, the curator of contemporary British art, said the installation was typical of the Chapman brothers' working practice in taking, absorbing and regurgitating previous pieces.
"We always have with them a sense of reworking and recycling. There's always this idea whereby whatever they make is something that can be possibly subverted or re-used - it can become a component for a new work."
Neither are the brothers afraid of the "Big Idea", whether it be artificial intelligence or the psychoanalytic theories of Freud.
In the case of When Humans Walked the Earth, they view the machines they have created as emulating biological and psychological states such as breathing, copulation and death.
"What they're doing is questioning the mechanistic theories of the mind, linking them back to the ideas of Sigmund Freud and psychoanalysis," Ms Wallis said. "But they're also interested in the relationship between man and machine and machine versus nature which they see as a false opposition. For example, there are a number of contemporary philosophers who see human consciousness in terms of computer models."
But in case that sounds too academic, there is always the subversive wit. Like naughty schoolboys lobbing inky missiles at the back of the class, Jake and Dinos Chapman frequently undercut their intense seriousness with a quite juvenile humour.
Although they have written books and participate in highbrow discussions about their work, demonstrating a more than passing understanding of contemporary critical theory, they take an evident delight in a joke.
In 1999, for instance, the brothers took their GCSE in art, entering themselves independently. Jake produced watercolour copies of the best known pieces of Brit Art, including Damien Hirst's shark. Dinos drew detailed still lives of skeletons of Siamese twins. Each earned a B grade.
And when they unveiled the Chapman Family Collection at the White Cube gallery of their dealer, Jay Jopling, in 2002, opening night visitors at first saw just the ornate carving of what seemed to be an ethnographic collection of African masks.
Only on adjusting to the dimmed light and looking more closely did guests gradually note the clown's grins and yellow arches of that symbol of the global age: McDonald's fast food restaurants. Yes, McDonald's has infiltrated the most remote corners of the world, including the art world.
Jake said at the time: "McDonald's is an attracter for so many different moral discourses on capitalism which are incredibly crude and funny - like the whole anti-globalisation thing, which is essentially a luxury of the West."
The brothers had created beautifully carved statues only to take a dig at global capitalism - and, perhaps, at liberal middle-class collectors of traditional tribal art.
Dinos Chapman was born in London in 1962 and his brother, Jake, in Cheltenham four years later. Their father was an art teacher.
They both graduated from the Royal College of Art in London in 1990, began working together shortly afterwards and quickly rose to prominence. The first works to attract attention were their three-dimensional recreations of Goya's series of etchings, The Disasters of Wars. They reproduced the graphic violence of Goya's work with life-sized figures, limbs hacked and mutilated.
The sexually-mutated child mannequins of Tragic Anatomies followed not long after, in 1996, again challenging the borders of taste. When that work was included in the now famous Sensation exhibition at the Royal Academy in London in 1997, subsequently transferring to New York, warnings were issued to parents. Julie Burchill branded the brothers "fascists" and New York Mayor Rudolph Giuliani called them "perverts".
The insults were, one suspects, like water off a duck's back. They thrived on controversy.
More followed in 2000 when their ambitious work Hell was the showpiece of the Apocalypse exhibition at the Royal Academy. A massive tableaux arranged in the shape of a reversed (Hindu) swastika, it comprised more than 5,000 tiny, model Nazis engaged in a surreal orgy of death and destruction.
Even the noted art critic Brian Sewell, who had publicly disliked much of their work hitherto, was converted by this when it was subsequently displayed by Charles Saatchi in his (now closed) Thames-side gallery.
"It is the grand operatic scale and scope of the Chapmans' joint imagination that horrifies," Sewell wrote in the London Evening Standard.
"There is in the brothers no hint of the aesthetic and intellectual exhaustion so evident in their contemporaries, nor the urge to turn aside from art, make films, run restaurants and succumb to the sad need to be celebrities, to expose and exploit their private lives. They strike me as men with a firm philosophical base, the pessimism of Heraclitus and the humour of Democritus, artists who will do ... what, as artists, they feel driven to do. They are that rare thing in our contemporary art world - genuine."
It was an extraordinary endorsement from a critic not easy to convince. Ironically it came just before the brothers were defeated in the battle for the 2003 Turner Prize, the most prestigious prize in British contemporary art, by Grayson Perry, the transvestite potter.
Although their Turner Prize show was not as lauded as many of their previous exhibitions, it must have been a bitter blow, nonetheless. Their initial reaction on the night was to strike Nicholas Serota, the Tate's director, with a lily. They looked keen to leaven the disappointment.
But the failure to win did nothing to stem their output. They have continued their experimentation with the works of Goya, painting over and augment 80 etchings from his Los Caprichos series.
Yet as if in acknowledgement of the importance of art, they were at pains when the work was launched two years ago to stress that it was etchings, not original paintings, that they were defacing - and that none of Goya's etchings were even produced in his own lifetime.
Doing a plausible impression of a responsible grown-up, Jake sounded a note of caution. "It would be very easy to try to be as vulgar as we possibly can be by getting our mitts on scarce, sacred objects [like paintings] but we're very conscious that the etchings are mass-produced objects," he said.
When the Tate announced its mid-career retrospective of the brothers' work last year, most of the art world deemed it entirely appropriate. Christoph Grunenberg, Tate Liverpool's director, thought it "surprising" the artists had not been so honoured before.
"Once you get beyond the surface shock of the work, you do realise it's incredibly intelligent and quite deep with big subjects of sex, death, the human capacity for violence and war," Mr Grunenberg said.
Ms Wallis said the retrospective proved they were "incredibly significant". "It's a really impressive show. There's an extraordinary body of work that really addresses issues of art and morality and contemporary society," she said.
The brothers seemed both appropriately grateful and eager not to get above their station at the honour. "I'm really pleased, but I would hope to give off a certain amount of modesty about the thing," Jake told The Independent.
"I'm sure it's the same with anybody who produces anything, anyone who writes or makes music, the reason you continue is because what you've produced isn't enough or it's an approximation to an idea or a failure of an idea. When you look at a retrospective, it's the sum total of everything that has forced you to feel that it's necessary to continue."
So continue they will as if in fulfilment of that other mordant wit, Samuel Beckett's, dictum: "Try again, Fail again. Fail better."
Bad Art for Bad People continues at Tate Liverpool until 4 March, admission £5. 'When Humans Walked the Earth' is at Tate Britain until 10 June, admission free. Another show of new work is planned for the end of the year at the White Cube gallery in Mason's Yard, London
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