For a country undergoing warp-speed modernisation, courtesy of billions of dollars of annual oil and gas revenues, one of the most fascinating transformations at work in Azerbaijan is also its most subtle. A few streets back from the polished perfection of Neftchilar Avenue – the Bond Street of its capital, Baku – and the Beaux Arts spires of the renovated Government House, honey stone façades are being carefully fixed onto communist-era apartment blocks, transposing the brute Soviet architecture of the Caspian Sea with the 19th-century pillars and elegant arches of Haussmann’s Paris.

Consequently, one spends a lot of time in Baku looking for clues to ascertain a building’s age, rather like checking for facelift scars behind the ears (those edifices in disguise still have their original 1970s windows). It’s symbolic of modern-day Baku, a place radically remaking itself as a modern city, with all the luxury shops, glitzy cocktail bars, major hotels and, perhaps most tellingly, contemporary art that go with such an endeavour.

Azerbaijan has a rich and ancient cultural heritage. The country’s lively mix of Islamic-European influences is the result of its geographic location at the lip of the Caspian Sea, its shared borders with Turkey, Russia and Iran, and a religious heterogeneity that means Islam, Judaism, Christianity and – in rare communities – Zoroastrianism are all practised here.

Historically, it’s a cosmopolitan spot. Azerbaijan was the first predominantly Muslim country to have a theatre, film studio and concert halls; in the 19th century Baku was dubbed the “Paris of the east” – visiting oil barons, the Rockefellers and Rothschilds, bequeathed the French villas that line the city’s esplanade. At night the buildings are lit as extravagantly as works in the Louvre; every pillar seems to have its own spotlight. As my driver from the airport remarks, “Baku is prettier at night.”

But art has always played a pivotal role in the city’s identity. Even under Russian rule, it flourished here. (Azerbaijan was incorporated into the Soviet Union in 1920, gaining independence only in 1991.) The winding, bazaar-like corridors of Baku’s Museum of Modern Art are filled with paintings in the Soviet realism style: bold canvases depicting oil labourers, cheeks smeared with black grease.

Still, the museum is a bewildering experience for those, like me, untutored in the country’s art history: captions are Pinter-esque in their brevity, and there is little evidence of curatorial influence. But exhibiting art in the London or New York mode is a new game to Azerbaijan. Baku is filled with galleries – small, atmospheric spots in the old city that trade in, mostly, traditional art or works by lauded national painters of the 1940s and 1950s. Contemporary galleries are few on the ground.

But not for much longer. Mila Askarova’s Gazelli Art House opened in November, the first commercial gallery in Baku dedicated to international art and run in conjunction with her Mayfair space. Askarova, who is Azerbaijani, opened the gallery with a show by New York-based duo Aziz and Cucher. She says, “Four years ago the art focus here was local to Azerbaijan or its neighbouring countries. We rarely looked to Europe or the rest of the world. But in the next three years there will be significant growth in the [international] art market in Baku. I opened there because I wanted to showcase artists that haven’t been seen in that region before.” She puts the sudden interest in contemporary art down to “the promotion of Azeri artists and culture outside the country, through exhibitions such as Phillips de Pury’s Fly To Baku.”

Of the latter, which opened in January 2012, Simon de Pury, former chairman of Phillips de Pury, says, “During my first trip to Baku with my wife, we visited many artists’ studios and discovered a vibrant and truly original art scene that we had been totally unaware of. The idea came up to do a travelling show, highlighting the work of some of these artists.”

The promotion of Azerbaijan’s contemporary art abroad has been spearheaded by the country’s ruling dynasty, the Aliyev family. President Ilham Aliyev’s glamorous wife, Mehriban, and her equally glossy daughter, Leyla, act as cultural ambassadors; both supported Fly to Baku, and Leyla is also editor-in-chief of Condé Nast’s Baku magazine, dedicated to all things of style and substance in Azerbaijan.

For Baku, the fresh focus on contemporary art appears to be part of a push for broader appeal, for international status as an equal to other east-west-melding cities such as Dubai, Beirut or Istanbul. Just as the Céline, Gucci and Tom Ford stores lining Neftchilar Avenue are statements of intent, so too is the vast, curvilinear, Zaha Hadid-designed Heydar Aliyev Cultural Centre (first picture), which opened in May 2012. To have the likes of the glass-fronted, minimal-chic Gazelli Art House on Nizami Street is, one imagines, as important to 21st-century Baku as the recently completed Flame Towers; by night these flicker-shaped buildings are lit by 10,000 LED lights that project images of licking flames and waving Azerbaijan flags. A Fairmont hotel will open shortly in one of the towers.

Baku is full of business travellers but, as yet, relatively empty of tourists. The old city, with its 12th-century Maiden Tower, stone mosques and rug shops, is rigorously kempt, its twisting alleys gorgeously atmospheric – but weirdly deserted. As a Russian friend who works for the Aliyev family tells me, “Baku can feel like a stage set with no actors.” I visited in November, when cold winds were barrelling off the grey Caspian, and went in search of – but did not find – an alternative, buzzing, modern café culture to counteract the blingy boutiques, a Lower East Side to Neftchilar’s Fifth Avenue.

There are less savoury aspects to the country, too. Azerbaijan is not known for its environmentalism: vast tracts of countryside are industrial wasteland and you would be ill advised to open your mouth while swimming in the sea. Its poor human-rights record was the subject of a damning Panorama documentary on BBC One, televised six days before Baku’s hosting of the Eurovision song contest in 2012.

Not that any of this is apparent during my stay at the cosseting new Four Seasons, an elegant, white wedding cake of a building fitted out with de Gournay wallpaper, marble floors, a gleaming spa and a ballroom with a reinforced floor (upon which wealthy Azeri newlyweds can drive their Ferraris). It was here, last September, that Christie’s showed a selection by the likes of Warhol, Picasso and Hirst (a work by Tamara de Lempicka at the Christie’s event is seen in the fourth picture) in a preview of a forthcoming London/New York/Dubai sale, flying over key clients, European museum owners, collectors and Christie’s chairman Viscount Linley.

The aim of the exhibition was twofold: to introduce this influential crowd to Baku’s art scene, as well as Christie’s to Azerbaijan’s collectors. The show was supported by the Yarat! Contemporary Art Space, an energetic non-commerical organisation established to organise, aid and exhibit Azerbaijan’s community of contemporary artists. Under directorship of the indefatigably enthusiastic – and model-beautiful – founder Aida Mahmudova, Yarat! has brought a new professionalism and vivid sense of excitement to Baku’s art scene. Its successes include a well-attended public art festival (to be repeated from next month; Mahmudova's Recycled installation from the festival is seen in the eighth picture), and a show that brought together Azeri and international artists of serious stature, including Sarah Lucas and James Turrell.

Yarat! recently opened a space called Yay! in the old city: “a commercial not-for-profit gallery”, Mahmudova explains. “All the profit we make goes to the artists and back into the organisation. The artists wanted to sell their work, but we couldn’t sell it through Yarat!. Also, Yay! means the artists aren’t mistreated. Many collectors still buy in the old way, through studio visits, and purchase works for very low prices. This way is better for the artists.”

Yay! is housed in a restored brick building in the old city. When I visit, an exhibition is being installed by the tiny, bearded, 25-year-old artist Ramal Kazimov, whose paintings of distorted human bodies in the grip of mental torment have a striking, Bacon-esque quality. “I’ve never sold a work before and I don’t think a lot of my paintings are suitable for the art market; I don’t think people will want to buy them,” Kazimov says. He’s wrong; they’re fantastic.

At the gallery entrance we run into one of the stars of the Baku art scene, Faig Ahmed, who is one of the board members of Yarat!. He shows me his work: traditional Azeri rugs, the weaving distorted so that patterns seem to bleed like Salvador Dalì’s clocks or warp into optical illusions. “I wanted to ask questions about identity,” he says. “Globalisation is changing the world, nations no longer have a distinct sense of identity. But our traditions are good and should be preserved.” Ahmed is one of the artists Mahmudova is taking to the Venice Biennale this year, to show in a pavilion of artists from the Caucasus. “When Azeris become rich, they start to buy art,” Ahmed says. “At first it’s mostly traditional, decorative pieces; but now the Azeri collectors are interested in contemporary art.”

Ahmed’s work featured in Fly to Baku (Section, 2011, second picture). So did those of Mammad Mustafayev, whose studio we visit in the attic of a nearby apartment block. The building is a Soviet relic: there are giant holes in the concrete steps, the lift shaft is a death drop and it’s pitch black at the top – we navigate by the light of our mobiles. (This is art-hunting as adventure sport, and clearly not for everybody. The younger generation of artists have moved to modern studios.) Mustafayev’s studio is filled with a lifetime of work – a path cuts through a deep drift of canvases, sculptures and paint cans, and cigarette smoke hangs in the air.

If Faig Ahmed represents the Azerbaijani art scene’s new guard, Mustafayev is the old guard. He speaks Russian to my translator and explains that for most of his life he worked under Soviet rule. “We never used to be able to exhibit our works outside of the country, but the current president is trying to improve the art scene here,” he says. “We have more freedom of expression now. I’m not being nationalistic; it’s the truth.”

Still, it seems that the government is not yet entirely au fait with contemporary art’s more radical aspects. At the 2011 Venice Biennale, the Ministry of Culture forced the advisory curator of the Azerbaijan pavilion, Beral Madra, to cover up a pair of statues by Azeri artist Aidan Salkhova – one of a woman veiled in black, the other depicting the black stone in Mecca that is sacred to Muslims. Madra wrote at the time, “Removing the sculpture will mean ‘censorship’ and it will do more harm to the image of the country than the sculpture itself. I think from now on this is the problem of the artists and curators living and working in Azerbaijan.”

Askarova takes a measured approach to the controversy. “The artist had many similar works upstairs at the pavilion that were very well received. I think curatorially it could have been done differently. I don’t know how popular these [contemporary] artists would be if they were to be quite obviously and directly anti‑government.” None of the artists I interviewed claimed to have ever felt their expression constrained by the government; in most cases, quite the opposite. As Faig Ahmed says, “Baku is much more tolerant now.”

There is, indeed, evidence of this around. To wit: the scenes of lithe Azeris dancing to DJs at Asian-fusion restaurant Chinar on a Friday night; the crowds drinking cocktails at Pasifico, or tucking into modern Azerbaijani cuisine at Sahil. The new, modish Marriott Absheron hotel (third picture) is packed with business travellers and out-of-towners, sipping tea in the reception or enjoying the wraparound views from the spacious bedrooms. The city’s Park Hyatt hotel (fifth picture) opened a new, three-storey spa last November, which features two swimming pools and indoor and outdoor tennis courts. In the old city, charming boutique hotel Sultan Inn offers an atmospheric escape with views of mosques, rooftops and cobbled alleys. Round the corner, at restaurant Caravanserai, men in moustaches and leather jackets eat aubergine salad and warm flat bread in front of a fire in the building’s original stone lodgings. Meanwhile, in the glorious Four Seasons, fashionable locals dine under gold chandeliers in the rooftop Kaspia restaurant (seventh picture). Down on the esplanade, birds sing from newly planted olive and eucalyptus trees.

This is a place whose subtle evolutions of the past few years have led it to the brink of major change, not least in the shape of the new airport terminal due this year, with direct US flights. And Christie’s is planning an exhibition of contemporary Azeri art this year, too. Already there’s an energising commotion around artists such as Faig Ahmed, Niyaz Najafov and Khanlar Gasimov, whose works are made in plaster, clay, photographic paper, sugarless candy or rosewater rice, on to which Sufi poets recite verses until they’re “absorbed” into the material (Gift Wrap, 2012, sixth picture). A lovely image for Baku, a place in mid-recitation; a place so much more interesting beneath the surface.