Beneath the bough of a blossoming tree, the beautiful couple stand arm in arm. Her white fur rustles against rough bark and her pearls tingle on silk. Her androgynous partner, in ruffled lace, with a straw hat and checked suit, his dainty geometrical moustache engraved on enamel skin, is still as a statue. They stare beyond us at – what?

The frame changes. Filigree branches tremble into abstract patterns. A boat rises out of the mist to hover on a flat lake, then its reflection dissolves into rippling lines. Over a bridge, up and down steps in a watery garden, under craggy rocks and fragile willows, past a cockatoo in a cage and a wild goat, the exquisitely dressed couple move on, high heels teetering, emotional balance precarious, as they drink in landscape and memory, time passing, love surviving or dying. Each frame, in chiselled black and white, is dizzyingly gorgeous, fluid yet stylised. You think all at once of Turner and Whistler, Monet, Seurat, Mondrian, the aristocratic belle époque and leisured self- consciousness of Jacques-Henri Lartigue or Marcel Proust; classical Chinese art's hazy pen-and-ink landscapes; the staccato nostalgia of 1920s silent movies.

No Snow on the Broken Bridge is an eight-screen monochrome film, shot on the banks of West Lake, Hangzhou, an area whose natural beauty has long lured Chinese painters and poets. It is theatrically installed at the upstairs gallery of London's Parasol Unit as a continuous half- circle, each large screen touching the next so that the whole thing unrolls like a giant Chinese scroll painting. This is the highlight of the first solo UK show by 35-year-old Yang Fudong and it introduces an artist who speaks in an original idiom, uses a modern medium, yet rivals the grand tradition of Chinese landscape art even as he plunders wildly from European modernist painting and photography.

If any 21st-century artist uses the camera like a brush, it is Fudong. He brings a lyrical, painterly sensibility to ravishing evocations of landscape and texture, making snow, fur, petals and flesh feel rich and exciting as they rarely do on screen, but he is also a master of film manipulation. Playing with time, editing the same picture of the boat's emerging silhouette to show it three times at different speeds, he disorientates while visually mesmerising us. Uncertainty – in the sexual ambivalence of his androgynous figures, the artful constructions of his mock- naturalistic scenography, a narrative that has no clear beginning or end – is everywhere and makes Fudong, for all his historical allusions, unmistakably contemporary.

In colour films here, Fudong shows that he can compete with the blaze and menace of much recent Chinese video and performance shock-art. Revival of the Snake features a blindfolded horseman of the Apocalypse hurtling on a white steed across fraught, spectacular terrain, now ice-bound, now a furnace. In the homoerotic Jiaer’s Livestock, two adjacent videos begin with men carrying a wooden pole from which one of their friends is suspended, bound to it with ropes in the traditional way for transporting a dead animal. A man in city attire, displaced in the pastoral scene, carries an "intellectual"'s suitcase. In one version he is killed; the second version has other murders, drownings, black humour and crude wit to contrast with the lush landscape.

Does Fudong fetishise Asian eroticism for the west? His theme, inescapable for 21st- century Chinese artists, is the collision of past and present in modern China, yet with this new work he has become a figure of international significance. His distinctive achievement, above all in No Snow, is to find a language for the regret, romance and melancholy that go with social evolution anywhere. Such bourgeois sentiments explain why cityscapes such as Flutter, Flutter, Jasmine, Jasmine, flickering poignantly between lovers in cheap rooms and aerial views of skyscraper-heavy Shanghai in transformation, recall the European tradition of poetic documentaries of city life, Baudelaire's or Manet's Paris or T.S. Eliot's London, "unreal city/under the brown fog of a winter noon". Like them, Fudong is an intoxicating chronicler of modernity in the making, deriving energy from a society in flux but drawing on the 21st century's global inventory of images.

Five hundred years earlier, at a time of political crisis and shifting allegiances in the eastern Mediterranean, the wily Doge of Venice sent his city's favourite painter, Gentile Bellini, to Constantinople as a diplomatic gift to Sultan Mehmet II. Though trading partners, 15th-century Venice and the Ottoman empire were in terms of travel and cultural difference as far apart as Beijing and London are today. Bellini imported the bright new technology of portrait-painting in oil to the Islamic world; in turn, as the National Gallery's lovely small exhibition Bellini and the East unravels, Byzantine motifs and techniques flooded his own art. In landmark works such as the portrait of a fur- and turban-clad Mehmet set within a stately arch, its parapet hung with bejewelled cloth, and a shimmeringly delicate watercolour of an Ottoman scholar at work, "Seated Scribe", coloured and gilded in Islamic style and inscribed in Persian, the Venetian painter introduced figures of unimaginable exoticism to Renaissance Europe.

In the televised Brideshead Revisited, Lord Marchmain (Laurence Olivier) presides over his palazzo and asks the ingénu Charles Ryder (Jeremy Irons) who is his favourite Venetian painter. "Bellini," answers Ryder impulsively. "Which one?" demands Marchmain. "I didn't know there were two," says Ryder, crushed, to which Marchmain triumphs: "There are three." Father and two sons, the Bellini dynasty not only provided successive official state painters to Venice but also controlled the workshop where both Titian and Giorgione were pupils. This show pinpoints how, in narrative paintings that minutely record buildings, costumes and personalities, the Bellinis and their followers came to define the republic to itself.

The show opens with a pair of portraits. In Gentile's depiction of middle-aged, stubborn, intellectual "Caterina Cornaro, Queen of Cyprus", the Venetian noblewoman who married the island's king is crowned with a cap embroidered with Islamic patterns, and looks steadily across at Giovanni's famous depiction of the corrupt Doge Leonardo Loredan. He is transformed by paint into a serene saint: the calm assurance of his expression, caught with gradations of light and shadow that blur contours and suggest a lofty presence, is matched by stately ceremonial robes made from a new import – damask, from Damascus – threaded with gold and painted roughly, in a then revolutionary technique, to catch the light and to gleam with a luxurious metallic shine. The eastern reference is picked up in "The Reception of the Venetian Ambassadors in Damascus", a monumental cityscape borrowed from the Louvre, which shows minarets, palm trees and merchants on camels and proclaims Venice's commercial links with the east.

Throughout the show, superb pairings underline just how influential Byzantine iconography was. The sumptuous silver and jewelled painted Orthodox reliquary that Cardinal Bessarion, a Greek exile fleeing the fall of Constantinople, gave to Venice is lent by the Galleria dell'Accademia to be reunited with Gentile's tender, dark-hued, moving painting of Bessarion praying before it. Cretan icons painted in tempera on wood, with their refined, elongated figures and glowing, red-gold tonality, are juxtaposed with Bellini Madonnas. Gentile's Virgin rests her feet on a lavish mosque carpet decorated with a niche to indicate the direction of Mecca, and is framed in an arch adorned with oriental ornamentation. Giovanni's downcast, oval-eyed, contemplative Madonna in a purple-cinnamon mantle hauntingly echoes the "madre della consolazione" of Byzantine tradition, and reminds one of the intense spirituality of Russian Madonnas.

Gentile’s coolly observed Virgin in her meticulous architectural setting belongs to the more sober early Italian Renaissance; Giovanni's emotional expressiveness and deep colouring predict Titian and Giorgione. But both fuse east and west, in a superbly focused show that cannot fail to have resonance in a Europe that is still seeking cultural links with Islam.

‘No Snow on the Broken Bridge’, Film and Video Installations by Yang Fudong, Parasol Unit, London N1, to June 3, tel +44 020 7490 7373.

‘Bellini and the East’, National Gallery, London WC1, to June 25. Tel +44 020 7747 2885