In a climate where the richest collectors – Charles Saatchi, Roman Abramovich – are as celebrated as the artists they buy, we tend to forget that in the history of arts patronage, entrepreneurs-turned-connoisseurs are a young development. The world's greatest museums – the Louvre, Hermitage, Prado – began as lavish civilisation-is-power statements by monarchs and emperors; private individuals did not emerge as significant museum patrons before the 19th century. Until a generation ago, those wanting to leave their mark in bricks and mortar usually did so in a room of their own – albeit a very grand one – in a state museum: the Duveen Galleries at Tate Britain, the Abby Aldrich Rockefeller Gallery at New York's Museum of Modern Art, the National Gallery's Sainsbury Wing. But in the past 15 years, that has changed: worldwide, collectors seek immortality in glass and steel, through a museum of their own, designed by an architect of their choosing.

These are not latter-day Henry Tates or Pavel Tretyakovs. Although they gave their names to museums, Tate and Moscow's Tretyakov were democratic visionaries who paid for buildings and donated core collections to kick-start evolving national, state-run institutions. Museum builders of the 1990s and 2000s, by contrast, are products of late capitalism, dedicated to more personal projects, with an individualistic flavour. They represent the legacy of Thatcher-Reagan mantras of choice, private philanthropy, me-generation celebrity.

Many of the new establishments are extravagantly specialist – Ronald Lauder's 2001 Neue Galerie in Manhattan, dedicated to German and Austrian art; Wal-Mart heiress Alice Walton's Crystal Bridges Museum of American Art, planned for Arkansas in 2010. And in recently capitalist nations, the symbolism of the private museum is heavy. Dasha Zhukova's museum of contemporary art, the Garage, launched in Moscow last month, trumpets the power of the new Russian billionaires. Guy and Miriam Ullens' contemporary art museum in Beijing, opened earlier this year, showcases the social and aesthetic transformation of a nation.

Together, these and scores more bring diversity and flatten old geographical hierarchies. In Istanbul, collector Sakip Sabanci's museum, founded in 2002, is the first ever to show western modernism – currently, Salvador Dali – in Turkey. Thanks to Dominique de Menil, the greatest collection of paintings by Cy Twombly, who lives in Italy, is on permanent show in Houston, Texas, in a gallery designed in 1995 by Renzo Piano. In 1996 the late collector and dealer Heinz Berggruen launched his Museum Berggruen in Berlin, giving Germany its only Picasso collection. This week, Charles Saatchi's new gallery opened in London with a show of recently acquired Chinese work.

Is all for the best in the best of all possible worlds? Certainly, more private museums mean more art on display for more people to see. Today's collectors are reluctant to bequeath to established museums, where space shortages mean works may go straight into storerooms and stay there. By contrast, a dedicated museum maintains the integrity of a collection, keeping together outstanding groups of works, assembled with personal flair, in buildings designed to enhance them. Renzo Piano's light, limpid 1997 construction for Ernst Beyeler's cherry-picked modernist paintings in Basel is the shining European example. For contemporary work, private collectors have particular advantages: free of state bureaucracy, they can respond quickly to the fast pace, and show work in ways that are too radical for traditional museums – in the confiscated-goods warehouse of a former drug enforcement agency in Miami, for example, that since 1996 has housed the Rubell Family Collection, ranging from sensationalist Chinese photography by Zhang Huan to Jeff Koons' vacuum cleaners.

What's not to like? Only that, whether they are stylishly successful or tediously tacky, today's rush of private museums is destabilising the art landscape. That they challenge the economics of taste may waft fresh air into art-history's ivory tower, but the speed with which new money shapes scholarly endeavour is daunting – witness the recent splash of monographs and retrospectives of Gustav Klimt, reckoned a minor Austrian symbolist until Lauder paid a record $135m in 2006 to install “Adele Bloch Bauer I” as “our Mona Lisa” in his Neue Galerie. Private museums speed up, too, 21st-century crises of shrinking art resources and growing demand. Will Asher B Durand's iconic American painting “Kindred Spirits”, for example, bought for $35m by Alice Walton from under the noses of the Metropolitan Museum and the National Gallery, who had banded together to try to keep it in a public gallery, speak to more people in Bentonville, Arkansas, or in New York and Washington? If you strengthen holdings in the regions, you inevitably dilute centres of excellence. But to tell art's histories, public museums need a concentration of important work; diminishing that is to the detriment of scholars and serious art lovers everywhere.

And if the new museums are not up to scratch? There is no polite way to say this: many private collections are far inferior to those in public institutions. They collapse standards and offer a vainglorious travesty of a cultural experience to a paying public. We all have our bêtes noires; one of mine is Fran?ois Pinault's disappointing art-as-fashion-emporium at Venice's Palazzo Grassi, launched in 2006 (another Pinault museum is planned for Venice in 2009).

Repurchasing, a bone in the throat

Repurchasing remains the mainstream in relics retrieving, other than donating or demanding.

The donation of relics is largely left in vain due to its heavy reliance on the holder's consciousness and ethical principles.

Demanding the return of relics sounds reasonable according to an international treaty that mandates relics plundered during the colonial wars be returned to their homeland. However, the treaty fails to impose any practical restriction on non-member states like Britain and America who actually hold large mounts of Chinese relics taken during wars.

Despite the Chinese government's strong resistance to buying back national treasures, repurchasing by unofficial Chinese parties remains the norm; while undeniably a bone in the throat, especially when the victim actually bears the burden. Non-governmental buyers mainly consist of social groups and institutions as well as a few wealthy individuals.

According to the International Herald Tribune's report, the mainland special fund was still under intense negotiations with Christie's, trying to stop the Rat and Rabbit bronze statues from entering the auction markets and get them back under a reasonable price.

"We do respect the business rules of auction companies as well as the operating mechanism of arts markets. But it's definitely unacceptable to put plunder under the hammer." Mr Zong said.

"The price is the major issue. We need a reasonable price right now."

So far, five of the 12 animal bronzes have returned to China. The Rat and Rabbit will probably be the last two appearing on the market. The remaining five, Dragon, Snake, Sheep, Cock and Dog, may have been destroyed in warfare or lost forever, experts suspect.