The turnip is one of the oldest and least glamorous of all the cultivated vegetables, the staple root of the Old World poor for the better part of three thousand years before the potato came from the Americas to displace it. Botanically it is Brassica rapa, a single species put to a remarkable variety of uses: the swollen, white-and-purple root that is the turnip proper; the tender leaf, eaten as a green; the flowering shoot, eaten as cime di rapa; and the small black seed, pressed for one of the oldest of vegetable oils. It belongs to the cabbage family and to the same species as several Asian vegetables that look nothing like it, the pak choi, the Chinese cabbage, the mizuna, and the choy sum, all of them forms of the one plastic and willing plant.

Unlike the almond or the pomegranate, the turnip was almost certainly domesticated more than once. The genetic evidence points to at least two independent beginnings: a western one, around the Near East and the eastern Mediterranean, which gave the European turnip and the turnip-rape oilseed; and an eastern one, in China, which gave the leafy vegetables and the East Asian turnips. From the western cradle the root turnip spread the length of Europe and the Near East; from the eastern cradle the kabu of Japan and the manjing of China descend. The turnip's varieties, all forms of the one species, are still used substantially and distinctly in the kitchen today: the round white purple-topped European turnip; the small, sweet, fine-grained Japanese kabu, and the great Shogoin of Kyoto from which the senmaizuke pickle is shaved; the heritage Teltow turnip of Brandenburg, a finger-sized delicacy once praised by Goethe; and the leafy turnip-greens, the cime di rapa of Puglia, the grelos and nabiças of Galicia and Portugal, and the turnip greens of the American South.

A persistent confusion must be cleared away, for it runs through the English language. The swede, or rutabaga, the large, dense, yellow-fleshed root that the Scots call the 'neep' and the Cornish the 'turnip', is not a turnip at all but a separate species, Brassica napus, a relatively recent cross between the turnip and the cabbage. The dishes of the British north that are made with 'neeps', the bashed neeps beside the haggis, the Orkney clapshot, the swede in the Cornish pasty, are swede dishes, not turnip ones; the true turnip, Brassica rapa, is the smaller, faster, more delicate root of this entry.

For the whole of antiquity and the Middle Ages the turnip was, across the temperate Old World, what the potato would later become: the cheap, bulky, reliable root that filled the winter belly of the poor and fed their beasts besides. The Greeks grew it as the gongylis and the Romans as the rapa and the napus; Pliny the Elder ranked it among the most important of all crops after the cereals and the bean, and the Romans carried it, with their roads and their farms, the length of their empire, into Gaul, Germania, Hispania, and Britannia, where it became a fixture of the northern field and the northern pot. Through the medieval centuries the turnip and its greens were the standby of the European peasant, boiled into pottage, mashed with butter, and stored through the cold months, until the potato arrived from the New World and, over the eighteenth and nineteenth centuries, pushed the turnip down the table and out into the field.

That banishment to the field was, paradoxically, the turnip's most consequential moment. In the agricultural revolution of eighteenth-century England the turnip became the engine of the Norfolk four-course rotation, the great improvement, associated with Charles 'Turnip' Townshend, by which fields once left fallow were sown instead with turnips to feed cattle and sheep through the winter, allowing the herds to be kept alive rather than slaughtered each autumn, manuring the land, and lifting the yields of the grain that followed. The humble fodder turnip thus underwrote the population growth that made the Industrial Revolution possible, the least romantic of vegetables at the root of the modern world.

Eastward and southward the turnip kept its place at the table where the potato never wholly conquered. In the Levant the white turnip is pickled with a slice of beetroot into the brilliant pink torshi lift that stands beside every plate of falafel and shawarma; in Persia the shalgham is simmered into winter soups and eaten with honey against the cold; in the Punjab and Kashmir it is the shalgam of the winter curry and the slow-cooked shab deg. In East Asia, where the leafy and turnip forms of Brassica rapa were raised separately, the kabu became one of the gentle, beloved vegetables of the Japanese kitchen, simmered in dashi and shaved into the great Kyoto pickle senmaizuke, and one of the seven herbs of the new-year rice porridge. And wherever Europeans carried the turnip, its greens went with it: into Galicia and Portugal as grelos and nabiças, and across the Atlantic into the American South, where turnip greens stewed with a smoked ham hock became one of the soul-food greens of the region.

The turnip is today a quietly global vegetable that has never quite recovered the central place it held before the potato, yet has never disappeared either, surviving in three distinct guises: the root, the green, and the pickle. As a root it is humblest in the West, a cheap winter vegetable for the stockpot, the pot-au-feu, and the lamb navarin, redeemed at the fashionable end by the small, sweet young turnips glazed in butter and the baby kabu of the modern restaurant. As a green it is a genuine staple still, the cime di rapa of the Puglian orecchiette, the grelos of the Galician pot, and the turnip greens of the American South, prized for the iron-rich, faintly bitter leaf and the 'pot likker' it leaves behind. As a pickle it is indispensable across the Near East, the shocking-pink torshi lift of the Levantine table being one of the most recognisable pickles in the world.

In the East the turnip keeps a gentler, more refined place. The Japanese kabu is simmered whole in a clear dashi until translucent, shaved paper-thin into the lacquered rounds of the Kyoto senmaizuke, salted into everyday tsukemono, and folded, as suzuna, into the seven-herb porridge eaten on the seventh day of the new year for health. In China the turnip and its preserved forms, the salty dàtóucài among them, season the noodle bowl and the congee; in the Indian north the shalgam is a winter curry and the heart of the Kashmiri shab deg. From the engine of the agricultural revolution to the jewelled pink pickle and the delicate simmered kabu, the turnip remains, five thousand years on, one of the most widely grown and quietly useful of all the vegetables the Old World tamed.