The migrant crisis has fuelled a backlash against the political establishment, but the wave of discontent also taps into long-standing fears about globalisation and a dilution of national identity.
How is this right-wing backlash reshaping Europe’s political landscape?
In recent years the far-right Freedom Party (FPOe) has shaken up the centrist consensus politics that dominated Austria for decades after World War Two. But in April 2016 it went further, pushing both main parties out of the running for the presidency.
The FPOe candidate, Norbert Hofer, won the first round of Austria’s presidential election in April and then secured around half the vote in the run-off vote on 22 May. The result was so tight, it was not immediately clear if he had won.
The president’s role is largely ceremonial. But Mr Hofer’s score reflected widespread voter frustration with immigration and the political establishment. Hundreds of thousands of migrants poured through Austria last year hoping to settle in Germany. Some 90,000 people applied for asylum in Austria itself – 1% of the population.
When the late Joerg Haider led the party it achieved its best ever result in 2000 and entered the government, causing enormous tension with EU partners.
European Parliament seats (MEPs): 4
Far-right party ELAM entered parliament for the first time in May 2016 elections, securing two seats from voters stung by the island’s acute financial crisis in 2013.
Affiliated to Golden Dawn in Greece which many observers see as neo-Nazi, ELAM has held demonstrations against Turkish Cypriots and migrants.
It opposes the idea of reunifying an island divided since Turkey invaded the north in 1974 in response to a Greek-inspired military coup.
Denmark’s immigration rules are among the toughest in Europe – reflecting the power of the Danish People’s Party (DPP), which came second in last year’s general election.
Its 21% of the vote was a record for the party, and now the ruling coalition depends on DPP support in parliament.
The Eurosceptic DPP also won Denmark’s European Parliament election in 2014 by a wide margin, with 27% of the vote.
The DPP opposes multiculturalism, as do nationalists in the rest of Scandinavia, where centre-left social democracy no longer dominates in the way it did for decades.
Denmark became a target of Muslim anger in 2005 when Danish newspaper Jyllands-Posten published cartoons depicting the Prophet Muhammad.
Controversially Denmark has given its police the authority to seize valuables worth more than 10,000 kroner (£1,045; $1,514) from refugees to cover housing and food costs.
The government has also cut migrant benefits and put adverts in Lebanese newspapers warning against migration to Denmark.
The nationalist Finns Party (previously the “True Finns”) came second in last year’s general election. Party leader Timo Soini is Finnish Foreign Minister, in a coalition government.
The party advocates strict immigration controls and argues that Finns, not migrants, take priority for social and healthcare spending. Its roots lie in rural Finland and it has championed welfare policies that give it a populist dimension.
Many political observers see Marine Le Pen’s National Front (FN) as the biggest nationalist challenge to Europe’s liberal democratic traditions.
Ms Le Pen is expected to make a formidable push for the French presidency next year. That is likely to trigger a repeat of tactical voting by the Socialists and conservative Republicans to block her.
The FN won 6.8 million votes in regional elections in 2015 – its largest ever score – but lost in two target regions after the Socialists pulled out and urged supporters to back Nicolas Sarkozy’s conservatives.
Marine’s father Jean-Marie Le Pen, the FN founder who was fined for Holocaust denial, shocked France in 2002 when he won through to the second round of the presidential election. Marine famously got him expelled from the FN in a family feud last August.
The FN has two seats in the French National Assembly (parliament) and in 2014 won the French European Parliament election, taking 25% of the vote.
Marine Le Pen is anti-EU, rejecting the euro and blaming Brussels for mass immigration, because of the Schengen free-movement policy.
In 2010 she told FN supporters that the sight of Muslims praying in the street was similar to the Nazi occupation in World War Two.
The Islamist attacks on Paris in January and November, which nearly 150 people were murdered, raised alarm about jihadists taking advantage of Europe’s open borders.
German politics has been shaken up by Alternative for Germany (AfD), a right-wing party launched in 2013 by economists opposed to the euro. Under leader Frauke Petry it has drawn ever more support by rallying against immigration.
The AfD’s success has been interpreted as a sign of discontent with Chancellor Angela Merkel’s open-door policy for Syrian refugees.
Last year Germany took in a record 1.1 million asylum seekers, many of them Muslims from Syria, Iraq and Afghanistan.
The AfD has seats in half of the German state parliaments, though none yet at national level in the Bundestag.
Ms Petry has called for “drastic steps” to prevent Islamist ideology spreading in Germany, including a ban on construction of new minarets. She says Islam “does not belong to Germany” – though Muslims who “practise their religion peacefully and privately” can be good citizens.
She sparked a furore when she suggested that border police should be empowered to shoot illegal migrants if necessary. Her deputy Beatrix von Storch backed that suggestion.
Stridently anti-Islam rhetoric came initially from Pegida, a mass movement that started in the eastern city of Dresden, then spread to other German cities.
Pegida regularly draws thousands of supporters at anti-immigration marches. Neo-Nazi groups are among the Pegida followers, who denounce “the Islamisation of the West”.
AfD MEPs: 2
The popularity of far-right Golden Dawn – widely considered to be a neo-Nazi party – has surged during Greece’s economic meltdown.
Members have been accused of serious crimes including murder. The party’s leaders went on trial in 2015 over the murder of anti-fascist rapper Pavlos Fyssas.
Yet Golden Dawn secured 7% of the vote in the September 2015 election, and it now has 18 MPs, making it the third biggest force in Greek politics.
Its vote was especially strong among people hardest hit by the crisis. The austerity demanded by Greece’s creditors turned many Greeks away from the political establishment.
The anti-EU party wants to expel migrants and has distributed food in poor areas – but only to Greek passport-holders.
Far-right Jobbik is the third strongest party in Hungary – it won 20.7% of the vote in the 2014 general election.
The party denies that it is racist, but has organised patrols by an unarmed but uniformed “Hungarian Guard” in Roma (Gypsy) neighbourhoods.
Jobbik says more must be done to tackle “Gypsy crime” and party members have also stirred controversy by making anti-Semitic remarks.
Hungarian flags dominate Jobbik rallies, along with the red-and-white Arpad stripes, which are often seen as an echo of Hungary’s pro-Nazi wartime regime.
With Jobbik support the conservative government of Prime Minister Viktor Orban erected a razor wire fence along its border with Serbia last year to keep migrants out.
Mr Orban and Slovak Prime Minister Robert Fico are suing the EU over its quota scheme for distributing migrants among member states. Both leaders say Europe has to defend its “Christian” heritage.
Jobbik MEPs: 3
Local elections last year delivered big gains to the Eurosceptic, anti-immigration Northern League (Lega Nord) beyond its Venice power base.
Since the party’s launch in 1991 it has called for the creation of a separate northern state called Padania, combining Veneto, Lombardy and some other regions. But today its emphasis is less on secession, more on boosting the northern regions’ autonomy and paying less tax to the central government.
The influx of migrants from North Africa has put a severe strain on Italy’s asylum infrastructure and revived the fortunes of the Northern League. Some of the party’s politicians have made xenophobic comments about migrants.
The party got 4% in the last general election, in 2013.
Geert Wilders, with his mane of blond hair, is one of Europe’s most recognisable nationalist politicians. His anti-EU Party for Freedom (PVV) has surged to the top of Dutch opinion polls.
He wants to stop Muslim immigration, arguing that Islam is incompatible with Dutch values. He wants the Koran to be banned in the Netherlands.
He is currently involved in a court case, accused of inciting hatred against Moroccans.
In the 2010 general election the PVV won 24 seats, making it the third-largest party.
The ultra-nationalist People’s Party-Our Slovakia of Marian Kotleba entered parliament for the first time this year, winning 14 seats.
Mr Kotleba has previously dressed in a uniform modelled on the Hlinka Guard, the militia of the 1939-45 Nazi-sponsored Slovak State. But now he wears corduroy casuals.
Immigration was a major issue in the election campaign, even though Slovakia has taken in very few migrants. Robert Fico’s Smer-Social Democracy party won – and he contributed to the anti-Muslim rhetoric.
Smer MEPs: 4; Our Slovakia MEPs: 0
The nationalist Sweden Democrats (SD) have challenged the traditional dominance of Sweden’s Social Democrats, a party associated with generous social welfare and tolerance of minorities.
The SD argues for strict immigration controls, opposing multiculturalism.
In 2014 the SD became the third-largest party, winning 13% in the general election. But they are shunned by other parties in parliament.
More than 160,000 asylum seekers arrived in Sweden in 2015 – the highest per capita rate in the EU.
In October 2015 the anti-immigration Swiss People’s Party (SVP) won the parliamentary election with a record 29.4% of the vote. That translated into 65 out of the total 200 seats in the lower house.
Switzerland is not in the EU, but is in Europe’s Schengen free-movement area, and has a high population of immigrants compared with its neighbours.
Support for the SVP has grown during the migrant crisis. For years the party has pushed for tough immigration controls, using controversial black sheep posters that opponents describe as racist.
It spearheaded a campaign to cap EU migrant numbers – and the Swiss voted to do so in 2014. But there is now EU-Swiss legal wrangling over free movement of workers, as the Swiss appear to be defying the Schengen rules.