Britain's cultural cathedral marks decade of triumph

It's attracted tens of millions – making contemporary art the hottest ticket in town. Tom Lubbock celebrates Tate Modern's 10th birthday

Oh, Tate Modern! It's one of the wonders of the modern age. Since the converted power station opened 10 years ago, it has redefined the modern art gallery. It has made 20th-century art, once a public laughing stock, into a milling visitor attraction. It has invented a mass audience for modernism. It's the sort of phenomenon you just can't argue with.

Sheer size is its fame. The building is sublime. Take the descending ramp, enter the vast soaring empty cathedral-dimensioned foyer, and, whatever else might follow, this already makes the visitor feel grand. Then there are the numbers. Initially designed to draw about 2 million a year, it has now an intake of 5 million. An extension is planned for 2012 to cope with these crowds.

And the crowds – how were they drawn and how were they converted? Once there was a time when modern art was nobody's idea of fun. The highbrows thought it was very serious. The lowbrows thought it was boring or ludicrous. But we have changed all that. Twentieth-century art has become an entertainment. Media-friendly contemporary art has played its role in this shift. But Tate Modern, with its enormous welcome to the public, has been decisive. Here was something to see, something big, something curious, on the river and free. And in the process, Nicholas Serota, Tate's Director, conceived the modern art gallery anew.

Part of its invitation is the new way in which it has shown art. At its opening Tate Modern unveiled an original hang. The gallery was no longer to be an archive of art history. In fact, it never had been – the Tate's modern collection was always very patchy. So, making a virtue of necessity, showmanship made up for scholarship. Historical progression, movement by movement, was abandoned. Big themes now ruled. Rooms jumped between periods. The place was filled with daring mixtures and connections.

A Monet pondscape might hang by a piece of land-art by Richard Long. Video pieces chattered among paintings. Room led into room by a process of free association. It has produced some brilliant visual coups, like juxtaposing the dynamic Futurist sculpture by Umberto Boccioni, Unique Forms of Continuity in Space, and Roy Lichtenstein's Pop-Art air-battle, Whaam! The flowing energy trails of the sculpture are exactly like the fuel explosions in the painting. No traditional curating would have allowed this surprise to emerge.

Of course there have been some memorable exhibitions too – Douanier Rousseau, Brancusi, Duchamp-Man Ray-Picabia, Matisse-Picasso, Edward Hopper, Rothko, Joseph Beuys, Louise Bourgeois, Gilbert and George. And there have been valuable oddities, like the paintings of the playwright August Strindberg, and some good surveys, like this year's Van Doesburg and the International Avant-Garde, which is still running. But these shows might have appeared in many major galleries around the world. Tate Modern doesn't begin to compete with MOMA in New York or the Pompidou in Paris.

What Tate Modern has offered uniquely is something else: those annual spectacles, opening each autumn, staged in the Turbine Hall. This Unilever Series opened with Louise Bourgeois' gigantic spider, Maman. It was followed by even more stupendous exhibits. There was Olafur Eliason's The Weather Project, with its great baleful solar disc of sodium light, hovering high, bathed in mists, and with a huge ceiling mirror doubling the visual volume of the space. People went to gaze into the light for hours, basked on the gallery floor beneath it, as if it were a real sun.

There was Carsten Höller's Test Site, five helter-skelters, great glass-and-metal tubes, looping and twisting through the Hall. It was probably the most popular of these shows, with queues of people at the entrances on each level, waiting to take the plunge and be delivered seconds later on to the ground floor. There was Doris Salcedo's Shibboleth, a deep earthquake crack, literally cut into the concrete floor underfoot, zigzagging wildly across the floor, like forked lightning, with branching cracks splitting off here and there.

This if anything is Tate Modern's trademark: pure theatricality, art that is verging or crossing over into fairground. And is there any limit now? Who would dare rein it back, or suggest that there are other values in art beyond fun? But it's not in fact these one-off spectacles that matter. They can look after themselves. It's the everyday collection we should be concerned by, and the way this approach has affected it. It is essential to Tate Modern's revolution. And it assumes that we the public will never need or want to really look again. And remember: these are great individual works, made by great artists, housed for our sakes in a place of looking.

Now think of Tate Modern. If you were looking for a particular work of art, you wouldn't have a clue where to look. You're not supposed to be able to. As a visitor, your business is not to know your way or command your own looking. You're supposed either to be toured by the random narratives devised by the curators or simply drifting from room to room. Or if you could find a work, you could never give proper attention to it. You would find it as part of some creative juxtaposition, that was maybe clever, maybe unbelievably stupid, but whichever, ultimately intrusive. You can't extract the work from the curators' games and programmes. The display itself is the work. The artwork is only the ingredient.

Go today. At first glance, it all feels dense, vibrant, abundant. The Tate Modern experience is as strong as ever. The showmanship is undiminished. These rooms are exciting places to look around and walk through. But they're not places in which to stop, and steadily address yourself to any particular object. The overall installation steals the show. And move on, move on, there's something else coming up! The result is a space that leaves little room for contemplation. It has changed modern art for the age of the short attention span. It is often beautifully done. In its way, it is an amazing achievement. But, sorry, an art gallery it is not.

The experts' favourites

Stephen Deuchar, Current director of The Art Fund, former director of Tate Britain

Self Portrait (Strangulation), 1978, by Andy Warhol, currently on show

"Warhol is perhaps most famous for creating iconic images of 20th-century celebrities, but in this work his gaze is turned upon himself, joining their number but in an atmosphere of threat. Death is never far away; the act of representation morphs into martyrdom. The artist's signature use of multiple images is subverted here, literally turned on its head. The anomalous print, together with the stark image of strangulation, echoes his darker, more erratic side."

Francis Outred, Head of postwar and contemporary art for Christie's Europe

Chicago, Board of Trade, 2000, photograph by Andreas Gursky

"When I was an art student at Chelsea, I'd go to Tate Britain a lot and look at my favourite works by David Hockney and Francis Bacon. When Tate Modern first opened, I remember walking in for the first time, and seeing four Andreas Gurksys on the wall. There were two on each floor, outside the exhibition areas. There were two that were placed beside each other that struck me: Chicago, Board of Trade and The Rhine II.

"Gursky is an artist who is very much driving photography forward in our time and to have his work up was a really clear statement by Tate Modern at the time. For me, these two works make me very much aware of the global nature of our world. He travels around a lot, trying to find points of civilisation that are uniform around the globe. Chicago is an image of a packed stock exchange. There are hundreds of traders, but you can't tell any of them apart. They have become insects. Their coloured jackets start to form their own geometry, and it resembles a work of abstract art. It's a huge-scale work, so you get a sense of being overwhelmed."

Antony Gormley, Artist

How It Is, 2009, by Miroslaw Balka

"It's a fantastic work that is there at the moment and it makes extraordinary use of the Turbine Hall in its unique, cul-de-sac character. It's also a truly open work; it has lots of references – historical references, references to disappearing, transport, to the Holocaust and to notions of collective deaths – but you are very much left to your own devices [on interpretation]. It's one of those works where the art is the ground, and you are the figure in it, so it's not about providing a representation but allowing you to have a realisation."

Alex Proud, Founder of Proud Galleries, London

The Weather Project, 2003, by Olafur Eliasson. The Sun, 2003, pictured left "This was my all-time favourite work just because I really enjoyed it. For me, the joy of it was thinking 'Gosh, the scale of this thing is pretty awesome'. I didn't lie on the floor like lots of other people did at the time. I'm too much of an old suit for that sort of thing. I also wanted to go down those helter-skelter slides that came to the Turbine Hall [by Carsten Höller] but my children were ill, and I didn't, something I regret now. Tate Modern deserve a pat on the back, just in terms of this amazing space."