It's an Olympic year for artists too, and first out of the blocks is David Hockney: A Bigger Picture at the Royal Academy. Like the athletes competing in London this summer, Hockney – now a veteran at 74 – has spent the past four years pushing himself beyond his limits in preparation for what could be the defining test of his career. The result is one of the most ambitious shows in the Academy's 244-year history: more than 150 works, some of them gargantuan, more than 80% of which have been made specially for this exhibition and the particular spaces of this light-filled gallery.  For Edith Devaney, co-curator of the exhibition, the most invigorating part of the process has been watching the new paintings emerge first-hand. "Like David, we didn't know what to expect, but we knew it would be exciting," she says. "I remember him saying to me when we started off this process, 'We won't get this wrong.' And I thought, 'No, we won't.'"  Hockney has always dabbled in landscapes – notably his photo collages of the Grand Canyon and Pearblossom Highway in the 1980s and 90s when he was still in the States – but they have been a sustained focus of his work since he returned to live in Bridlington, East Yorkshire a decade ago. In recent years he has produced paintings at a complusive rate, first with watercolours then oils, and most recently on his iPhone and iPad. "David's not actually that interested in technology, he's just interested in other methods you can use to make art," she explains. "The work he did on his iPhone is charming, but the work he does on his iPad has the painterly quality of his oils – it's astonishing."  Another new direction for Hockney is his use of film. Showing as a world exclusive at the Royal Academy his films are created by nine high-definition cameras pointing in fractionally different directions – the result has been described as a "moving cubist collage".  "It has the same multiplicity of perspectives," says Devaney. "When you look at this film you feel as though you are seeing the world through David Hockney's eyes."  With Hockney's canny knack for self-promotion – he recently declined to paint the Queen because he was "very busy painting England actually, her country" – marketing expectations for the show are off the scale. As a private and independent institution, the Royal Academy is not obliged to supply a projected attendance, but there are whispers that A Bigger Picture could challenge the 1999 Monet exhibition, which hosted 813,000 visitors. Demand was so relentless back then that the Academy opened its doors 24 hours a day, a UK first. "In principle we'd do that again," says Jennifer Francis, head of press and marketing. "Certainly in the final few weeks, if we think people will be there at three in the morning."  Advertising for the show will have local, national and international targets – from buses in Bradford to the LA tourist board. "It's the first time I've bought space on buses up and down the country," says Francis. "There is a massive buzz about this exhibition."  "I really sense the position of this exhibition in history," interjects Devaney. "It's a slight change of direction for us: we are picking someone like David, who is at the height of his powers, and giving him freedom. Working very closely with him, but allowing him to take off. In 100 years' time people at the Academy will look back and think, 'Oh my God, this was a really important thing for the Academy to have done.'"  David Hockney: A Bigger Picture is at the Royal Academy, London W1, 21 January-9 April  The cynical among us might wonder if the National Portrait Gallery's auspicious Lucian Freud: Portraits exhibition was hastily conceived in the aftermath of the artist's death last July. We would, however, be missing the mark by, ooh, about five years. "The idea came to me in 2007, just after we won the Olympic bid," says the National Portrait Gallery's contemporary curator Sarah Howgate. "Everybody felt it would be a fantastic exhibition to do in 2012, when Lucian was going to turn 90. Our director, Sandy Nairne, told him, 'You are going to be our Olympian,' which Lucian found quite amusing."  Howgate can also measure the complicated gestation of the show in another way. "I started writing to lenders in 2008 to request his work and then I went off on maternity leave," she recalls. "Now my little boy is three and the exhibition is just about to start!"  There are 132 works in Lucian Freud: Portraits, the largest exhibition of his portraiture that has ever been assembled. Howgate secured almost all of the key paintings that she requested from museums and private collections, including Benefits Supervisor Sleeping, bought in 2008 by Chelsea FC owner Roman Abramovich for £17m, a world record auction price. Other coups include one of Freud's grandest works, Large Interior, W11 (After Watteau), not seen in the UK for a decade, and Portrait of the Hound, his final, unfinished painting.  "It's a balancing act for lenders," says Howgate. "Works, which quite often hang on their walls, have to come down for a year and that creates quite a gap. But on the other hand their work is going to be hanging in this really important exhibition in a great venue, so it's prestigious to be part of it. And it's happening at a time when the world's attention is going to be on the UK and London in particular."  The NPG is anticipating around 160,000 visitors, which would match the number that came to see David Hockney Portraits: Life Love Art in 2006 (also curated by Howgate), their record for a paid-admittance show. Denise Vogelsang, head of marketing, advises booking in advance and coming in the morning; an "early-bird offer", for example, gives you two-for-one tickets for the first slot of the day. "But the show takes over pretty much the whole of the ground floor," says Vogelsang, "so it's a bigger space than we normally have and we can accommodate a larger number of visitors without it feeling too crowded."  Howgate is adamant that Lucian Freud: Portraits be viewed as "a celebration, not a memorial", and she points out that the artist had seen and approved the paintings that are being shown, even the layout of the exhibition and the merchandise. Nevertheless, it will be almost impossible to view the show, which spans 1939 to 2011, without speculating on Freud's colourful personal life. His two wives and assorted lovers are prominently featured, and it sometimes feels that you can see relationships deteriorating over the course of their sittings.  It will also be hard not to consider Freud's legacy as you wander round. "It's just really sad that Lucian isn't going to see it because he would have been incredibly moved by it," says Howgate. "Obviously his family are all going to come, so it's going to be an emotional time for them and that is going to make it all the more powerful. There was a feeling in the art world that a real master had died, and I think it will become even more clear that we have lost one of the greatest realist painters of the 20th century."  Lucian Freud: Portraits is at the National Portrait Gallery, London WC2, 9 February-27 May  The venerable National Gallery was just five years old in 1829 when JMW Turner wrote a will leaving his entire oeuvre – more than 1,000 works – to the nation. The artist had just one stipulation: when he died, he wanted a pair of his own paintings (Dido Building Carthage and Sun Rising Through Vapour) hung between two landscapes (what he called The Seaport and The Mill) by a baroque artist who had inspired him more than any other, Claude Lorrain. The request is still honoured to this day, in the cosy, octagonal room 15, but in March the National Gallery is preparing a much grander statement of the affinity between the two masters.  Turner will be the draw for most visitors but Jill Preston, the National Gallery's head of communications, believes that Claude's mastery of light and composition will be a revelation. "We're hoping that a lot of people out there will, through the Turner name, be introduced to Claude for the first time," she says. "Outside the art world a lot of people who are not familiar with Claude will find his work absolutely delightful, really inspiring."  Turner was formally introduced to the work of Claude, who died almost a century before he was born, when two of his landscapes came through London in 1799. These paintings, along with Turner's sketches of them, open the exhibition. "They really caused a splash those two Claudes, they were what everybody was talking about," says Susan Foister, deputy director of the National Gallery. "The sketchbooks record Turner's reactions to these works and he refers to them again and again throughout his career because it's material he can keep reusing but making different each time. This room really sets the scene for their relationship."Turner Inspired: In Light of Claude might seem the most traditional of the big 2012 shows, but the National Gallery believes it has much to intrigue enthusiasts of Hockney, Freud, even Hirst. "Our show "is about looking backwards and forwards at the same time," she says. "Turner saw that you could look at a work painted decades earlier and make something very different of it. That's what artists go on doing and I think that's what Turner was showing he could do with Claude."  Preston is determined to spread the word that the gallery is becoming more rounded, less stuffy even. The programme for 2012 includes a show where contemporary artists, dancers and poets respond to three works by Titian. Friday Lates, where the collection and shows stay open till 9pm, offers live music, debates and a roomful of people sat cross-legged with pencils and paper doing a Talk and Draw session. "We would like the process of discovering an exhibition to be an active one," she says.  "Five million people come to the National Gallery each year so variety is very important."  Turner Inspired: In the Light of Claude is at the National Gallery, London WC2, 14 March-5 June  Everyone in the art world agrees: the factor that has by far the biggest impact on the success of an exhibition is the fame of the artist. This is probably why Marc Sands, director of Tate media and audiences, can't help smiling broadly as he talks about Damien Hirst's first UK retrospective, opening at the Tate Modern in April. "It will be the most talked-about show of the year," he predicts. "The name recognition couldn't be much higher. I've never met more people with a view on an artist. Largely it tends to be more on the artist, whom they have probably never met, than it is on the work that many of them have never seen."  The 46-year-old Hirst will always polarise opinion, Sands concedes, but he hopes visitors can suspend judgment until they see the work, dating from 1988 to the present day. "The divisive nature will only make the discussion, the debate, the interest more prickly and more alive," he says. "I already know what some newspapers will say, but the public should decide for themselves."  For the curator, Ann Gallagher, Tate's head of collections, the exhibition started with a single work: the 14ft tiger shark suspended in formaldehyde or, if you prefer, The Physical Impossibility Of Death In The Mind Of Someone Living from 1991. "For obvious reasons, it's a piece that everyone would want to see," she says.  Most of Hirst's most notorious pieces will also be among the 70-odd works: there are spot and spin paintings, medicine cabinets and the £50m platinum and diamond skull, For The Love Of God, will be displayed in the Turbine Hall for the first 12 weeks. There's also a room devoted to the works he sold for £111m at Sotheby's in September 2008, the day before Lehman Brothers disintegrated. But Gallagher is keen to draw attention to lesser-known exhibits. She is particularly excited by the reconstitution of 1991's In And Out Of Love, which fills two rooms with hundreds of tropical butterflies, some of which are spawned from canvases on the wall.  There is no room in the exhibition for Hirst's recent, little-appreciated skull paintings, but there will be at least one new piece. Gallagher, however, remains tight-lipped as to what form it might take. "You have to leave something as a surprise." There has already been controversy earlier this month with reports – subsequently denied – that David Hockney had criticised Hirst for his over-reliance of assistants. For the Tate, he has been a model collaborator: "Damien's very involved, he's very busy, but he has a good team," says Gallagher. Sands has found him "hands-on, but with an incredibly light touch".  Any rivalry between Hockney and Hirst is likely to be settled after the summer by visitor figures. Sands is quietly confident. "If you come to London as a tourist, you're likely to go to Buckingham Palace, Tate Modern, the British Museum and Camden market," he says, "not necessarily in that order." Gallagher has a much simpler ambition: "I'd like people to come and actually look at Damien Hirst's work," she says. "Whatever they may have heard about him previously, just look at the work."  Damien Hirst is at Tate Modern, London SE1, 4 April-9 September
As the works go up and the buzz begins, Tim Lewis speaks to the movers and shakers about how they got here …