Human migration is as old as history. Even migration to distant places and remote cultures is nothing new. In the nineteenth century, millions of Europeans sought liberty and prosperity in the Americas, notably in the United States. What is new today is the scale of migration, often across huge cultural divides - and often without a definite aim.
The African boat people in the Mediterranean are often not even sure whether they want to be in Italy, Germany, or Britain. Even those who are certain, like North Africans in Spain and France, or Turks in Germany, had as their priority escaping the hopelessness of their home countries, not arriving at a particular destination.
This modern form of migration raises massive problems for countries on the receiving end. In Europe, it is probably the most serious social issue today, because no one has a clear idea about how to manage the resulting clash of cultures.
Once upon a time, North America, notably the US, seemed to provide the answer. It was that of the "melting pot": different peoples made their own contribution to American culture, but, above all, they made every effort to accept what they found and integrate. "No," the Russian woman who came to the US in the early twentieth century replied to the grandchild who asked whether her ancestors arrived with the Pilgrims on the Mayflower. "Our ship had a different name, but now we are all Americans."