Out of an azure sea rise sheer cliffs, their clefts woven with tapestries of green and red bushes, and white gulls swoop and soar in the balmy air.

As a pleasure boat edges closer, strange rock formations arch up from the lazily lapping Tyrrhenian Sea, and sea caves entice its passengers into the island's mysterious vaults. But what can't be seen is even more powerful in its effect: the legends of antiquity, the aura of famous residents, the gossip and scandals, the works of art created here, the smell of money.

Mythic isle, a destination for hedonists since classical times, its reputation for beauty and luxury ramped sky-high by Hollywood stars in the 1950s and 60s, Capri has a unique status in European tourism as a peerless idyll of eternal magnetism. A rocky rectangle only 7km long and 3km at its widest, lying offshore from the Sorrentine peninsula at the southern end of Italy's Bay of Naples, Capri has drawn day-trippers since the mid-19th century and package tourists since the 1950s. Surely, therefore, the magic has gone, once you step ashore?

Not so. Especially if you dock at the smaller harbour, the Marina Piccola, on the quiet south side, rather than the hydrofoil- and megayacht-packed Marina Grande, on the north coast. At Marina Piccola the beach of translucent blue waters is out of a dream, and above it steeply rises an amphitheatre of dense greenery, dotted with villas, capped by cliffs.

A road zig-zags upwards to the town of Capri, which sits on a saddle in the east of the island. Suddenly, things look bad: the narrow streets are crammed with tour groups wandering from pretty little shop to chic designer store. Still, it's undeniably cute; a whitewashed warren of tiny lanes and hidden houses, a tightly built village that could shut itself up quickly when the warning came that Saracen pirates or other marauders were on the way - the stark reality for many centuries.

Take a narrow alley that winds upwards and soon you breathe again. The best direction is east, towards Monte Tiberio, the 300-metre-high headland on which Emperor Tiberius spent his last days in an opulent villa. Walking along winding paths where motor traffic is banned - and could hardly fit, anyway - you pass exquisite white villas draped in a profusion of flowers and surrounded by unusual shrubs: a botanical paradise. The sweet scent of honeysuckle fills the air as the climb wends gently upwards, to reach the pine forests of a cliff-top nature park.

The heights are occupied by Tiberius' ruined palace, Villa Jovis, a place where, the classical gossip-mongers say, he indulged in elaborate orgies while ruling the vast Roman empire. Not much is left of a once ornate mansion; instead, rumours fill the air - of the pool where he soaked as children nibbled his flesh; and of the unfortunates who displeased him and were flung from the clifftop.

Today, the only power up here is that of nature, and it is overwhelming: fabulous cliff-edge views down to turquoise bays far below, with russet, yellow and green shrubs clinging to the rock faces, and seagulls keening and gliding in the pine-perfumed air.

On a tree-fringed promontory far below, a curious red building, long and flat-topped, catches the eye. Casa Malaparte was built by Italian author Curzio Malaparte in the 1940s and became a cinematic icon in the 60s, as the setting for Jean-Luc Godard's Le Mépris (" Contempt"), with Brigitte Bardot sunning herself on the roof of the villa while a writer, a producer and a director argue about their film project, based on Homer's Odyssey. So seductive are these waters on Capri's south side that many believe the Greek poet's sirens lured sailors to shipwreck from the rocky islets here. So potent were the sirens' calls that Odysseus had himself lashed to the mast to foil them.

In the 50s, when Capri was the very height of fashion, sirens of the silver screen fetched up on the island in great numbers. Ingrid Bergman, Audrey Hepburn, Elizabeth Taylor, Rita Hayworth, Jane Russell, Grace Kelly and Lana Turner, the A-list of that era's movie goddesses, all holidayed here. If you sat long enough, it was said, at a cafe table in La Piazzetta - the little square at the heart of Capri town - you'd see everybody who was anybody.

Today, the celebrity scene seems to rotate around designers by the name of Hilfiger, Armani, Ferragamo or Swarovski, all of whom have both villas and stores on the island. Leonardo di Caprio and Beyoncé stroll the streets or lounge at an exclusive pool, but other sights are more mesmeric than they, would the celebs not agree?

In Anacapri, the island's less-developed half, a chair-lift carries riders to the highest point, Monte Solaro. They sway over vegetable gardens and citrus groves up to a magnificent panoramic view of Capri, the Sorrentine coast and the whole Bay of Naples. Near the summit lie the remains of a British fort built during the Napoleonic wars, and there's a cafe with a deckchair terrace and a suitably elevated name: La Canzone del Cielo ("song of heaven").

Down at the far end of Anacapri, under low cliffs, is the sight that ignited Capri's tourism, the Blue Grotto. A sea cave entered by rowing boat, the grotto's water and roof are bathed in an exquisite electric blue light, an effect of sunlight beaming in through the narrow entrance. The ultimate symbol of Capri's spellbinding beauty, in the late 19th century, the Blue Grotto drew famous artists to the island for extended periods, writers such as Alexandre Dumas, Oscar Wilde, Henry James and Maxim Gorky, and composers Mendelssohn and Debussy. Italy's claim to Eden, they called Capri.

The artists were followed by northern Europeans of wealth and taste who built luxurious villas, an elite band of aesthetes and sybarites who revelled in Capri's classical associations, its natural beauty and liberal ambience. The names Friedrich Alfred Krupp and Baron Fersen still resonate on the island through beautiful places they created - and the scandals around them.

Boss of the mighty German steel company, Krupp built a vertiginous zigzag path - Via Krupp - from Capri town, where he stayed in the Grand Hotel Quisisana, down to a seaside grotto, where he choreographed orgies with local youths. Jacques d'Adelswärd-Fersen, a wealthy poet fleeing a sex scandal in Paris that also involved boys, built his Villa Lysis (aka Villa Fersen, free entrance) high on a cliffside, and enjoyed its neoclassical and art nouveau beauty with a young Italian Adonis as his partner.

Axel Munthe, a renowned Swedish doctor of spotless reputation and philanthropic bent, left a particularly fine legacy. For a taste of the good life of Capri's foreign residents a century ago, a visit to his former clifftop home, the Villa San Michele, is a must. Incorporating Roman remains in a kind of Romanesque style, the house and grounds are studded with classical statuary. From its vine-entwined pergola there are breathtaking views over the Bay of Naples.

"Layabout Land" (Apragopolis) for the Emperor Augustus, the island's original second-home owner, poeticised to "Land of Sweet Idleness", Capri lives up to its legend, and that's not a frequent thing in today's world.

Getting there: Turkish Airlines flies from Hong Kong to Istanbul six times a week, and daily from the Turkish city to Naples. There are daily helicopter and ferry services from Naples airport to Capri.