Dansk Folkeparti (Danish Peoples Party) arose because of the established primarily left leaning political parties completely ignored and froze out the party to begin with.
The biggest political party, the Social Democrats (also likes to call itself the workers party) lost touch with it's voters when society in general went from production sectors to service sectors. A rising unrest about immigration manifested itself in a lot of voters who didn't benefit from the immigrants coming and taking jobs or just living of welfare that many danish voters felt they paid for (Denmark have extreme taxes)
And so while the political establishment tried to ignore them they slowly grew to become now the second biggest political party in Denmark. However now for other reasons than muslim immigration. The reason now is that DF is the only party that really takes the average joes concerns seriously no matter how primitive they might seem to many.
Today most parties are in line with DF as they have recognized that you can't just take in a lot of people and then expect them to become a natural part of society.
Denmark has one of the most honest debates about immigration and it speaks volume about the level of political corectness and control over the media in other countries that even though Denmark is one of the countries who take most immigrants and refugees, spend most money on immigration both domestically and internationally and has some of the most extensive rights for immigrants it still had to defend it's political line in the EU.
Denmark is fairly clear on what it's doing. There are many bad things I can say about my home country but I actually think that debate wise we have some of the most free and civilized debates especially considering the hot topics we often discuss.
See for example [0] (Swedish) and links within.
http://www.dn.se/nyheter/sverige/internationella-medier-sver...
The populist complaint against rightist politicians in the United States is that they claim to oppose illegal immigration, but that's actually just a scam to fool the rubes into voting for them. When push comes to shove, they quietly endorse the current (Democratic) administration's policies on the matter and make sure that efforts to block them always fail. Given that, the factors behind Trump's support aren't so different from the factors behind support for populists in Europe.
DF is gaining because ordinary people are seeing their jobs being outsourced or underbid by eastern european citizens. In fact this is today the primary reason for why parties like DF gets more and more power. They are the only parties who actually takes peoples concern seriously. There is a much much bigger fraction of the western society who do not stand to benefit from technological progress, multicultural society and globalized workforce.
If anything what is happening right now is a national conservative trend where people who aren't benefitting will vote on the parties that are sceptic to progress.