“Every American who has ever lived, with the exception of one group, was either an immigrant himself or a descendant of immigrants,” wrote a young senator in 1958. The senator’s name was John F. Kennedy, himself the grandchild of Irish immigrants.

Since the country’s founding, immigration has been one of its most contentious and controversial issues. In addition, many who have come to the U.S. came against their wills, as slaves, and many others who wished to enter the United States were barred for reasons ranging from foreign-policy issues to stereotypes to the prevalent political atmosphere of the time. As a result, the most common origins of American immigrants have shifted over the years, and some groups are better represented than others.

But no matter where an immigrant comes from, the challenges of moving don’t end on the day he or she enters the United States: Once in the country, legally or illegally, naturalized or not, immigrants face tough decisions on how to present themselves, whether to give up their names or native languages, and what being “American” means for them. As a result, the immigration experiences of some Americans—even those the country embraces as icons—can be obscured. Here are the stories of eight American icons you might not have realized were immigrants:

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