Amorgos has two ports at opposite ends of its long body: Katapola in the middle, where the big Blue Star ferries from Piraeus call after a voyage of around nine hours, and Aegiali at the northeastern tip. The road between them is rough enough that locals will tell you it is often faster to hop back on the ferry than to drive. Above Katapola sits Chora, the whitewashed capital, perched some 400 meters up in a saddle with sea on both sides. A Venetian fortress crowns it, a reminder that for three centuries after 1207 this island answered to Venice before it fell to the Ottomans.

People have lived on Amorgos for an extraordinarily long time. Tombs here have been dated to around 3300 BC, and in the Early Cycladic period three separate settlements grew along the northern coast, each founded by a different people: Naxians at Kastri in the southwest, Samians at Minoa above Katapola, and Milians near Aegiali. The island even gave Greece a poet of its own kind. Semonides — born in Samos but the founder of a colony here — was one of the great early practitioners of Greek iambic verse, writing in the 7th century BC with a biting, unsentimental wit. His most famous surviving fragment is a satirical poem on women, comparing their natures to various animals. Few small islands can claim a hand in shaping an entire poetic tradition.

For centuries the women of Amorgos made embroideries so fine they commanded high prices far beyond the Aegean and propped up the island economy. The very best of that work no longer stays here. Some of the finest surviving pieces hang in the Victoria and Albert Museum in London, displayed as the textile art they always were. What is sold in the shops today is lovely, but the islanders are honest that it does not match the standard of those earlier generations, whose patient stitching turned needle and thread into a living.

In the late 1980s the French director Luc Besson came to Amorgos to film "Le Grand Bleu," released in English as "The Big Blue," a story of two rival free-divers. The movie became a cult sensation across Europe and made this once-anonymous island famous overnight. Besson's cameras lingered on the white monastery of Hozoviotissa clinging to its cliff, on the beach at Agia Anna below it, and on the rusted shipwreck in Liveros Bay. Decades later, divers and dreamers still arrive chasing the color the title promised, and the water rarely disappoints them.

Amorgos rewards those who slow down. Old marble-paved donkey trails crisscross the island, still polished by hooves, linking villages and hidden coves. Hike up near Aegiali at sunrise, or down to a beach you reach only on foot, and you will likely have it to yourself. End the day with a glass of psimeni raki, the local spirit steeped with honey, cinnamon and cloves, poured to welcome guests, including, by tradition, those who have just made the long climb to the monastery and earned it.