There are few parts of the animal, from intestines to tongue, that haven't found their way onto the menu at St. John in London. When chef Fergus Henderson opened the restaurant in 1994, London's most coveted tables were still devoted to French sauces, foams and nouvelle cuisine's tiny portions. Henderson went in the opposite direction, serving the unfashionable foods he'd encountered in Italy and France – skate, anchovies, tripe and kidneys among them – and he has stood by the same nose-to-tail principle for thirty years: "If you're going to kill the animal, it seems only polite to use the whole thing.” Tom Harris, who worked at the restaurant for over a decade, put it more bluntly, calling the now-iconic restaurant "a fuck you to all that was haute."

St. John's signature dish, roast bone marrow and parsley salad on toast, was inspired by the gluttonous bone-sucking in the 1973 film La Grande Bouffe, and the late Anthony Bourdain deemed it his death row meal. He first visited the restaurant on the recommendation of A.A. Gill, and by the end of the meal he was "tottering unsteadily into the kitchen, getting on to [his] knees and bowing down in front of Fergus." He called Henderson's book, Nose to Tail Eating, "a cult masterpiece" and credited it with "completely expanding the larder and giving chefs permission to cook the parts they'd always wanted to cook."

Before it ended up in the rarefied world of London dining, offal was, for centuries, what you ate when you couldn't afford the premium cuts. The wealthy took the sirloin and the fillet, while the poor were left to make do with the leftovers: liver, kidney, tongue, heart, brain and lungs. Through the war and the long years of rationing that followed, offal was often the only meat going, and by the time rationing lifted in 1954 it had become the flavour of austerity. A steak was a sign the hard years were over. Then supermarkets arrived with their pre-cut, plastic-wrapped meat, pushing offal further to the margins.

"Before it ended up in the rarefied world of London dining, offal was, for centuries, what you ate when you couldn't afford the premium cuts. The wealthy took the sirloin and the fillet, while the poor were left to make do with the leftovers: liver, kidney, tongue, heart, brain and lungs."

Now, it turns up in some of the world's most inventive kitchens. Irish-born chef Max Rocha trained under Henderson and head chef Farokh Talati at St. John before opening Café Cecilia, where he still runs the kitchen on the same nose-to-tail logic. Once a week, a whole pig or lamb comes in, and the team breaks it down together. "It's a really nice way for the whole team to learn butchery," he says. At Fallow in St James's, cod's heads that were once discarded are now served with sriracha butter and have become the menu's centrepiece. In Sydney, Josh Niland has built Saint Peter around a simple question: why does a nation surrounded by ocean throw away half of every fish it catches? The same instinct has turned mirror dory eyeballs into chips and kingfish milt into mortadella.

It's not the first time culinary fortunes have turned. Until the mid-to-late 19th century in America, lobster was so abundant it was used as fertiliser, fishing bait and rations for prisoners and indentured servants, where, legend has it, some servants even negotiated clauses in their contracts limiting how often they could be fed the crustacean. Boiled into a mushy paste and quick to spoil, the "cockroach of the sea" carried real stigma. Then the railroads brought wealthy inland tourists who'd never heard of its reputation, and by the 1920s the pauper's ration had reached white tablecloths. Caviar underwent a similar transformation. 19th-century American sturgeon roe was also so abundant that bartenders piled it onto free sandwiches to encourage men to drink more before overfishing turned it into one of the world's great luxury foods. Food writer Emiko Davies says the pattern goes back much further. "When you go back to the Middle Ages, truffles were for peasants too," she says. "One, because they were free, and two, because they came from underground, like potatoes or onions, so they were seen as only fit for peasants."

Nose-to-tail cooking is just one expression of a much broader tradition in Italy: cucina povera, the peasant cooking from which many of the nation's best-known dishes emerged. Few chefs have carried its philosophy further into the world's most celebrated kitchens than Massimo Bottura. The Modena chef behind Osteria Francescana traces it back to his Grandmother Ancella's kitchen. She never measured anything, cooked by memory and by love, and he remembers it now less as any single dish than a feeling: the smell of tortellini in broth on a Sunday morning, the sound of the rolling pin on the wooden table, hands repeating gestures passed down for generations. Every week she collected stale bread in a glass jar; on Sunday evenings it became passatelli, one of the most comforting dishes of his childhood. "She wasn't trying to be sustainable; that word didn't exist in our vocabulary then," he says. "She was simply respectful. Respectful of food, of the work behind every ingredient, and of the people around the table."

For him, the same ingenuity gave rise to ribollita, feijoada, cassoulet and countless other dishes, all born from the same simple question: "How can I make something extraordinary from what I already have?". That idea runs through his book Bread is Gold, where Bottura argues that the transformation of humble ingredients begins in the way we see them. "A great cook doesn't add value through cost, but through ideas, culture and care," he says. "Creativity begins with constraints. When you stop asking, 'What am I missing?' and start asking, 'What is possible with what I already have?'

"Cucina povera was never about being poor," he continues. "It was about being resourceful… and the belief that nothing should be wasted." Today, he thinks, the problem runs the other way: "We have access to almost everything, all the time. Yet that abundance often leaves us disconnected from the true value of food." He points to his Grandmother, who never thought in terms of leftovers, only possibilities. "It's wisdom," he says. "In a world obsessed with having more, cucina povera teaches us how to do more with less."

"Food has become important to express not only cultural identity but also distinction, social status, the fact you're cool and cosmopolitan. Traditional foods like offal have become exotic for people of a certain class living in cities."

Rachel Roddy, food writer, cookbook author and Guardian columnist, has spent years writing about cooking born of necessity. She grew up inside the tail end of Britain's offal tradition, in the kitchen of her Granny's pub in Lancashire, The Gardeners Arms, where a menu of oxtail stew and ox tongue sandwiches kept patrons from drinking on an empty stomach. In 2005, she moved to Testaccio – Rome's old slaughterhouse district – and found her own childhood waiting for her on the menus and in the atmosphere of the city's trattorias. A distinctive style of cooking developed there in the 1890s, known as quinto quarto, or "the fifth quarter": the parts of the animal left after the prime cuts had been taken. Slaughterhouse workers were partly paid in these leftovers, and it was they, or more likely, their wives, who worked out how to turn them into something delicious for dinner.

"Offal is the epitome of cooking out of necessity, and when it's cooked well, it's fantastic, but you really have to be good to cook it well," she says. Only through rediscovering it in Rome, and cooking it herself, did Roddy realise what a "competent and careful" cook her Granny had actually been. "I'm so intrigued by it, because offal cooked badly really is disgusting," she says. Take tripe, which "smells of shit when it's raw, and still stinks when you boil it; to cook it requires real skill." Some historically maligned ingredients, in other words, are not inherently bad so much as badly cooked. Brussels sprouts, boiled into oblivion in many Australian kitchens in the 1990s, have undergone a similar rehabilitation in recent years, thanks in part to chefs like Yotam Ottolenghi.

Roddy is wary of the term cucina povera, seeing it as tangled up with marketing, PR and what she calls a "mad galaxy of invented tradition." "It can be a really helpful term," she says, "but we need to reframe it a bit. I prefer the term 'everyday cooking' or 'people's cooking'. Looking at it as intelligent cooking that's evolved over time takes away the romance of poverty." She has spent the past five years travelling through every region of Italy for her upcoming book, and the deeper she went, the less romantic the history became. "I've been confronted again and again with the immense poverty in every region in Italy," she says. "Call it 'cucina povera', or 'the food of poverty' if you want, but it was actually famine."

She is just as clear-eyed about tradition itself. "Recipes are always, always evolving," she says. "Food is an evolving language." The idea that Italian food can be reduced to a set of fixed rules is, in her view, "absolute codswallop." The best trattorias, she says, are the ones that remain attentive to the present: where a new generation keeps the bean soup but changes the bean supplier; where the old pasta recipe survives with a new flour; where natural wine appears on the list; where the menu might be traditional or innovative, but you can feel that it belongs to now. "They're ancient ways of cooking, with a modern state of mind."

Bottura shares that philosophy. "Tradition isn't a museum," he says. "It's something alive that has to evolve if it wants to survive."

Take Florence's iconic lampredotto sandwich. "They eat a lot of lampredotto, or fourth cow stomach, in Florence," Roddy says. "It's one of the city's most iconic street foods, real 'cucina povera', and there are trucks everywhere selling it. "The word 'lampredotto' comes from a fish," she says. "Talk about appropriation. The rich people used to eat fish, and the poor made tripe into 'fish'." The very best lampredotto in Florence right now, she says, is a mushroom sandwich made the same way by a vegan chef. Lampredotto purists are furious, insisting he has no right to the name, to which he has a ready answer: do they actually know the word's history? "It's such a perfect example of cucina povera," Roddy says. "But it's a totally stolen word to begin with. The aristocrats in Renaissance Florence were furious when the poor people started cooking disgusting offal like their beautiful lampredotto fish."

For all its reinvention, this kind of cooking still asks something of the cook: the soaking, the simmering, the cajoling of cheap and readily available ingredients into something extraordinary. So, what does Roddy make of its popularity among a generation with more choice and convenience than any before it? "We're united by instinctive good health," she says. "Not health as fanaticism, but simply what the body already knows it needs. We've known since the Greeks and Romans that a diet built on vegetables serves us well, and the dishes cucina povera left behind, like pasta and beans, braised tougher cuts, bean and vegetable stews, are exactly that. When I say good health, I'm also talking about pleasure, function, and sustainability."

Twenty years after moving to Testaccio, Roddy is watching her neighbourhood change. "Tripe and chicken breast still have equal importance at my local butcher," she says. "But offal is expensive now. It's no longer the cheapest cut."

Fabio Parasecoli, author and professor of food studies at N.Y.U., grew up in Rome yet has seen the same pattern play out around the globe, most recently in the pine forests of southwest China. In Yunnan, towards the Tibetan plateau, matsutake mushrooms grew wild and were mostly ignored for generations. Then Japanese merchants started buying them: in Japan, the mushroom marks the beginning of autumn and commands a serious price. A picker in Yunnan earns thirty or forty dollars a kilo for a mushroom that, at a Tokyo auction house, has in a good year fetched close to a hundred thousand. "The people that gather it do not eat it," he says. "Because for them it makes more sense to send it out to get cash."

Nostalgia is one force that can turn a humble food into a desirable one, he says, and it isn't always first-hand. "There is a chickpea and chestnut soup I grew up eating every Christmas, from my Grandparents' region of Abruzzo," he says. "For me it's a dish of nostalgia. Younger generations didn't grow up eating it because their parents stopped making it, yet in their twenties they experience this sort of 'vicarious nostalgia'."

It's only part of the story, though. "Food has become an important way to express not only cultural identity but also distinction, social status, the fact you're cool and cosmopolitan." It's also, he thinks, a reaction against globalisation. "Let's say we all eat the same thing. Everything is mixed; everything is fusion. Any dish that could claim some sort of adherence to a past, to a tradition, to a cultural group is a plus."

“Cucina povera can be a really helpful term, but we need to reframe it a bit. Looking at it as intelligent cooking that's evolved over time takes away the romance of poverty.”

Davies, who has lived in Tuscany for more than 20 years, suspects economics is bringing people back to this way of cooking as much as evolving tastes. "We are reaching a point where we will have to cook like our Grandparents did: frugally," she says. "The cost of living is rising everywhere you look, and cucina povera is an inspiration because it shows that you can cook and eat well by spending less. You use local ingredients, more legumes, vegetables and starches, less meat, and more stale bread. You don't waste a thing if you can help it." For her, the shift goes beyond the grocery bill. "You can feel better about the planet too, because cucina povera is inherently sustainable."

Nikolina Skenderija, food anthropologist and head sommelier at Cantina, a zero-waste restaurant built into the cliffs above a pebbled beach on the Greek island of Sifnos, sees another impulse at work. Fermentation, pickling and smoking were once ways of keeping food from spoiling; now the same instincts show up in organic markets, sourdough workshops and natural wine bars, places with no shortage at all. "Is all this because we are poor?" she asks. "Or because we live in abundance? Peasant foods? More like a modern eco-asceticism." Still, she thinks the impulse behind it is a good one. "We must keep on telling stories in books, plates, or wherever," she says, "because stories are the sweetest bite we can melt on our tongue."

In her home country of Bosnia, cooking from necessity is still a living memory. She tells me about the Sarajevo-born, Lisbon-based chef Ljubomir Stanišić, who arrived in Portugal in 1997 and has since become one of the country's most celebrated culinary figures. He keeps a handful of Bosnian dishes on his Michelin-starred restaurant's menu, most of them made from potatoes. During the war, his family had very little, and his Mother didn't want to frighten her children by revealing the extent of their economic precarity. "Potatoes were the cheapest food back then, so she made them for him every day, but differently," Skenderija says. "One day as a mash, another in the oven, then rolled in phyllo dough." He keeps those dishes on his menu now, she says, "not only because he wants to celebrate them, but also to show the transforming potential of food, and humans."

It's the kind of transformation Bottura has spent his career championing. A chef's cultural influence, he argues, misses the point if it's used only to create luxury. He sees his three-Michelin-star Osteria Francescana and Food for Soul – the non-profit he founded that turns surplus and discarded food into meals served in community dining rooms called refettorios – as two versions of the same idea. "People often think one is about luxury and the other about necessity," he says. "I don't see it that way. Excellence isn't defined by the price of an ingredient; it's defined by the intention behind what you do." Whether he is serving The Five Ages of Parmigiano Reggiano in Modena or a meal made from ingredients that would otherwise be thrown away, he says he is asking the same question: "How can food become a vehicle for culture, empathy and change?"

"For a long time, we confused luxury with excess," he continues. "Today, I think we're finally understanding that true luxury is consciousness. It's knowing where food comes from, respecting the people who produce it, and using every ingredient to its fullest potential." The next wave of chefs, he says, are increasingly "proud to tell the story of an onion, a crust of bread or a forgotten cut of meat."