Alpert has traveled widely as an investigative journalist, and has made films for NBC, PBS, and HBO. Over the course of his career, he has won 15 Emmy Awards and three DuPont-Columbia Awards. He has been nominated for a 2010 Academy Award in the category of Best Documentary, Short Subject for China's Unnatural Disaster: The Tears of Sichuan Province. He has reported from Vietnam, Cambodia, Iran, Nicaragua, the Philippines, Cuba, China, and Afghanistan.

In 1972, Alpert and his wife, Keiko Tsuno, founded the Downtown Community Television Center, one of the country's first community media centers. He has interviewed Fidel Castro several times, and was one of the few Western journalists to have conducted a videotaped interview with Saddam Hussein since the Persian Gulf War.