From Milan, to Marseille, to Madrid and in so many other cities across Europe, streets have erupted in colourful, passionate protests in recent weeks. While most started peacefully, a large number ended in shocking scenes of violence and looting. There have been allegations of radical left-wing groups sparking riots intentionally and reports of police heavy-handedness.

We've seen thousands rallying in Rome and Florence. Hundreds of thousands across France. In Madrid, an encampment of tents has occupied a city-centre square since late September. In Lisbon, tens of thousands of mostly young people marched earlier this month. Tear gas and water cannon were used on protesters in Brussels, after young men dressed in black, their faces covered to hide their identities, threw rocks and firecrackers at police. In Albania, demonstrators alleging government corruption are demanding that their Prime Minister Edi Rama – already 13 years in power – stand down. This continent feels volatile, socially and politically.

I've spent years in Europe reporting from a multitude of demonstrations, both peaceful and violent. I remember well the ardent Catalan pro-independence marches of 2017, the desperation and Molotov cocktails flying through Athens' streets during the 2015 Greek debt crisis, and various outbreaks of violence in France during President Emmanuel Macron's first term in office, sparked by fuel tax and pension reform proposals.

But this feels different. Protests are exploding simultaneously across Europe and the majority of demonstrators – both peaceful and violent – are young. Some really young. Among those arrested, there's an eyebrow-raising number of minors. Over half of those detained in Barcelona scuffles last weekend were under 18. Minors were among those apprehended by police in Milan after clashes, according to Italy's LaPresse news agency.

Europe's governments, for the most part, have been careful to distinguish between looters and rioters on the one hand, and loud but peaceful, legally organised demonstrations on the other. The latter tend to focus around a particular cause. In the current protest wave, placards and chants mainly take aim at education grievances, social inequalities and the rising cost of living – though each country also comes with its own unique set of complaints.

What has triggered this public fury in Europe's youth, seemingly so quickly? Are all these demonstrations in some way interwoven? And with major European elections on the horizon, how will governments choose to respond – listening to protesters' concerns, or playing the law and order card to win support from older voters?

Students have taken to the streets in France, Belgium, Ireland, Spain, Portugal, Italy, Greece, Serbia and Albania – a more than 1,000-mile span of the continent.

Demonstrations are often organised in an ad hoc way via TikTok or Instagram. Belgium's interior minister has complained about what he calls the "TikTokisation" of protests.

Student unions play a role in organising marches, but they are also inspired by the actions of peers in other countries, even other continents. Think of the so-called Cockroach student movement in India – a Gen Z social and political protest movement that emerged in May this year, starting with criticism of the Indian education system.

France, where the current wave of student protests kicked off in late September, fuelled by student complaints over staff shortages and dilapidated buildings, is a stand-out catalyst in Europe. There's a saying in neighbouring Belgium: whenever it pours in Paris, it at least drizzles in Brussels. The Belgian capital and the town of Liège have also now seen weeks of protesting youngsters.

In Barcelona this weekend, students were encouraged to demonstrate under the social media hashtag #InstitutsIndignats, echoing the French slogan, Lycées Indignés (Outraged High Schools).

In Athens, 17-year-old Greek school pupil Yiannis Papanikolaou told AFP: "School buildings are terrible and poorly maintained… I think something might change, because of what France is doing, France will spur Greece." There's a continent-wide sense of economic malaise felt by large numbers of young people – and it goes far beyond education. They worry about the environment, and fret that AI will rob them of job opportunities. They fear the spiralling cost of living could prevent them from finishing their education and stop them buying or renting a home big enough to start a family.

In Madrid and in Lisbon, frustration has focused on the prohibitive price tag attached to housing. Portuguese Instagram-linked campaigns stated "enough is enough" and called on people to take to the streets as peers had done in Spain.

In Lisbon, Carolina Cruz, 26, a PhD student and biology researcher, said she faces losing her home as her rental contract nears expiry. "I'm the first person in my family to enter a doctoral programme and even with all the studying I've done, I still can't make it," she told Reuters.

It's an anger shared by 22-year-old Riccardo, a protester in Italy's financial capital, Milan. "Even if we don't manage to throw the country into chaos like in France or block every road like in Spain, the aim is at least people will start talking about these issues again," he told AFP.

And it's certainly not just young people on the left of politics who are angry. At the presidential campaign launch of French nationalist Marine Le Pen last weekend, young supporters described different concerns to me. Calling themselves the "silent majority" – not (yet) out demonstrating – they say they also worry deeply about "uncontrolled immigration" and safety on France's streets, as well as the cost of living.

The outpouring of discontent has spread beyond young people to include trade unions, France's disparate Yellow Jacket movement that protested against the cost of living crisis during Macron's first term, and other citizens' initiatives. This weekend, Kent in coastal southern England saw two protests, one for and one against immigration. This miscellaneous mix of protests can seem confusing.

Mark Leonard, the director of the European Council of Foreign Relations, speaks of a build-up of cascading, competing crises in Europe, none of which have ever been properly resolved, he says. That sense of pent-up anger is now bubbling over onto the streets.

"One crisis layers on top of the other," he told me. "The financial crisis of 2007-8, the migrant crisis of 2015, the environmental crisis, Covid, inflation after Russia's full-scale invasion of Ukraine in 2022 and now again with the war in the Gulf." Leonard says different "tribes" have emerged out of these crises. Social media consumption and algorithms harden their differing perspectives, leading to a real sense of polarisation in Europe.

"We've already seen this in the US," says Leonard. "A sense of 'my crisis is more important than your crisis'." Nathalie Tocci, a former Italian government adviser who is now a politics professor at Johns Hopkins University, tells me we shouldn't be so taken aback by the protests, or the youth engagement in them.

"We tend to think of youngsters as politically switched off and disinterested. We think they don't bother to go out to vote etc, but they are truly engaged," she told me, "just in a different, more grassroots way. Think of the "Fridays for the Future [environmental movement] across Europe a few years ago, or the demonstrations against Israel's actions in Gaza after 7 October.

She points to the student-led protest movement in Serbia, which recently defeated long-standing leader Aleksandar Vučić in parliamentary elections. "It's quite something. They kept going and going, for more than two years. What sticking power will these new European street demos have? That's not yet clear."

And what about the looting and the violence? Intelligence services in France and Belgium have described looting on the edges of legally approved protests as mainly opportunistic.

The rioting, they suggest, is a mixture of "mindless violence" – also identified by the Spanish authorities in Barcelona to describe clashes there at the weekend - plus mayhem intentionally orchestrated by youth from ultra-left radical groups.

Tocci reminded me that, in Italy, you can hear the word "maranza" being used by some Italians upset by the perpetrators of destruction seemingly for the sake of it: smashing or burning cars or public bins, for example.

In France, rioters are often described as "casseurs" – people who break things. But in private, some use a more politically charged term – "racaille". Like "maranza" in Italy, it's pejorative slang, generally used to describe disaffected, rowdy urban youths frequently from working-class and/or immigrant backgrounds. It was used in October 2005 by then-French Interior Minister Nicolas Sarkozy, to describe young delinquents and rioters during a tense visit to the housing projects of Paris suburb Argenteuil.

French media has also asked whether there's been an alliance of convenience, however informal or incidental, between two groups of youths: ultra-left activists and young people from France's disadvantaged neighbourhoods. Like the anti-capitalist left, youth from public housing projects on the outskirts of French cities (known as the banlieues) often feel discriminated against, and complain of police heavy handedness towards them.

The political right and centre in France, including Macron, blame left-wing radical groups and "delinquents" for planning the riots. In contrast to Le Pen's National Rally Party, they have not mentioned a link with past or current immigration to France.

Critics accuse anti-immigration parties in Europe of trying to capitalise from the riots to score political points. In Belgium, the anti-immigration opposition Flemish nationalist party, Vlaams Belang, appeared to blame migrants for violence in Liège and Brussels, describing the riots as "imported" and blaming a failure of integration and of open borders. Belgium's Interior Minister Bernard Quentin has pointed the finger at ultra-left groups. Fresh mass demonstrations have been planned over the next days in France and in Italy.

Governments are trying to crack down on the violence. There have been thousands of arrests, and Italy and France have promised to impose a "you break it, you pay for it" policy for rioters.

Italian Prime Minister Giorgia Meloni is also making parents of minors liable for damage caused by their kids, including deducting welfare support received by the family. The Civil Code in France already holds parents who live with their children liable for damage they cause.

But some of these European governments may not be in power for long. All the big EU countries have been holding, or will hold, key elections in the coming months. France's presidential vote is considered the most pivotal for Europe. Le Pen is consistently polling far ahead of her rivals. It's assumed the unrest on French streets is helping her, thanks to her party's law and order message.

In Spain, Italy, Germany and Poland, nationalist, tough-on-immigration parties are also polling well. These parties promise to restore order and national pride. Leonard believes populist or non-traditional parties on the left and the right have become "crisis entrepreneurs", using the turbulent situation in Europe to attract disaffected voters.

Meanwhile, Europe's political mainstream faces a crisis of leadership, says Grégoire Roos, director of Europe at the Chatham House think tank.

I would argue they also face a crisis of legitimacy. The fact that so many people - the young and not so young - are out protesting indicates they have failed to get on top of things.

But it's not at all clear that new elections will resolve public frustration. France is so polarised, for example, that if Le Pen were to become president, many predict her opponents would fill French streets in anger.

Modern Europe is built on an assumption that citizens pay taxes and obey laws. In exchange, they get good public services, like education and healthcare, personal safety and a stable society that follows certain rules and regulations. But this "social contract" has clearly eroded, says Roos. Looking at the ferment on Europe's streets, this moment of protest looks likely to continue.

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