More than 40 years after arriving in New York from Mexico uneducated and broke, Felix Sanchez de la Vega Guzman still can barely speak English. Ask him a question, and he will respond with a few halting phrases and an apologetic smile before shifting back to the comfort of Spanish.

Yet Mr. Sanchez has lived the great American success story. He turned a business selling tortillas on the street into a $19 million food manufacturing empire that threaded together the Mexican diaspora from coast to coast and reached back into Mexico itself.

Mr. Sanchez is part of a small class of immigrants who arrived in the United States with nothing and, despite speaking little or no English, became remarkably prosperous. And while generations of immigrants have thrived despite language barriers, technology, these days, has made it easier for such entrepreneurs to attain considerable affluence.

Many have rooted their businesses in big cities with immigrant populations large enough to insulate them from everyday situations that demand English. After gaining traction in their own communities, they have used the tools of modern communication, transportation and commerce to tap far-flung resources and exploit markets in similar enclaves around the country and the world.