London's Brick Lane Mosque started as a church for Protestants hounded from Catholic France — for whom the word "refugee" was first coined. Later, displaced Jews turned it into a synagogue. Today, Muslims kick off their shoes in the lobby before prayers.

That layering of migrants over centuries, like strata in rock, tells a story vital for Europe to remember as it struggles with new flows of people seeking sanctuary and fresh starts.

Viewed historically, Syrians, Iraqis and others risking their lives to become European are simply marching in step with what has long been a tradition on the continent: uprooting and moving. A perpetual trample of feet — from town to town, country to country, landmass to landmass — helped create the resilient, textured, rich Europe now so appealing to asylum-seekers, by blending people, ideas and technologies.

European travelers have covered the broadest possible range, from intrepid medieval merchants like Marco Polo to today's twenty-somethings who grew up on a borderless continent and crisscross it on low-cost flights for anything from a football match to love, jobs and more.

Across the continent, migration's marks remain visible like footsteps in snow. Moscow's Kremlin, for example, resembles Milan's Sforza Castle because Italian artisans helped rebuild the fortress in the 15th century. And in 16th century Vienna, Italians introduced chimneys and built up the new industry that ensued: chimney-sweeping, said Annemarie Steidl, a University of Vienna migration expert.

"There are still chimney sweeps in Vienna, if you look in the phone book, who can trace their ancestors back to these Swiss-Italians," she said. "It's the story of Europe ... One group after another arriving, blending in and changing our society."

What exactly the latest newcomers contribute will depend, in part, on how they and their hosts adapt to each other. Like previous settlers, they must contend with fears that they'll siphon away jobs, housing and other resources. But in putting down roots, they and their offspring will add strands to Europe's tapestry.

"Each time there was an intense resistance and a notion that 'You don't belong here, you're invading us,'" says Columbia University sociologist Saskia Sassen. "Then they become incorporated and build one of the layers."

Assimilation isn't a given. Race riots in 1950s England, mobs chasing African immigrants through streets of southern Spain in 2000 and immigrants' children torching cars in three weeks of rioting in France in 2005 showed the process can be spectacularly fraught.

Even outsiders culturally and ethnically similar to their hosts triggered allergic reactions, even murder. In 1893, rampaging Frenchmen killed and injured dozens of Italian laborers working the salt flats of southern France. Huguenot Protestants — the original "refugees" — who escaped 17th century France were both welcomed and eyed warily in Britain. And "because they were different," floods of Czech-speaking migrants initially provoked fear in 19th century Vienna, but then "completely blended in" in two or three generations, said Steidl.

That process will also work with would-be Europeans arriving now, she predicted.

"These people will be European. But Europe will be different," she said. "Migrants are changing us and we are changing the migrants."

With Indian parents and an English heart, Sunny Bhopal embodies that idea. His Indian grandfather who moved to England in 1975 started the fabric store, piled from floor to ceiling with hundreds of rolls of cloth, where Sunny works opposite the Brick Lane Mosque.

The London-born 27-year-old roots for India when it plays cricket, but feels "more English" when he travels there.

"I don't feel like it's the place for me," he said. "Home is actually back in England."

The melting into the mainstream of Paris' once large and distinct community of Spanish migrants also shows how quick integration can be. In what used to be known as "Little Spain," on the northern outskirts, a chapel and theater that catered to them are now closed. There's still a cultural center where Spanish-speaking retirees meet but it isn't such a strong magnet for their France-born kids.

"One day or another it will disappear altogether, if there isn't a new wave of large-scale immigration," said Gabriel Gaso, director of a French umbrella group of Spanish associations.

Syrians, other newcomers and their hosts are now embarking on this journey together. They've met with both outpourings of help and with hostility, notably from Hungary's prime minister, Viktor Orban, who declared: "If we let everybody in, it's going to destroy Europe."

Yet Europe would be very different without migration. Had their ancestors not left Ireland, The Beatles might not have met in Liverpool. Albert Einstein might not have become a Nobel prize-winning physicist without his migratory path of schooling and discovery from Germany to Italy, Switzerland, back to Germany and finally to the United States. Had Angela Merkel's paternal grandfather, Ludwig Kazmierczak, not moved to Berlin from what is now Poland would she have become Germany's chancellor and been so sympathetic to those now beaching on Europe's shores?

The Huguenots repaid England's welcome by enriching it with industry, notably silk-weaving. As they melted into society, their church began its transformation into a metaphor for human layering, becoming a Methodist chapel, the Great Synagogue and now the mosque.

"Imagine London without its great tradition of welcoming strangers who have always proven, ultimately, to be a huge benefit," said historian Dan Cruickshank. "London without that would be a bleak and sad provincial place."