Block graduated from Harvard University in 1983 with a degree in French history and literature and in 1984 was a Fulbright scholar at the University of Geneva. She is married to former Wall Street Journal reporter and NPR sports contributor Stefan Fatsis. They have a daughter and live in Washington, D.C.. She started with All Things Considered in 1985 as an editorial assistant. She later worked as editor, director, senior producer, and then as a correspondent in New York. Her 1999 report investigating rape as a weapon of war in Kosovo was cited when NPR News won an Overseas Press Club Award. Her September 11, 2001 reporting was part of coverage that earned NPR News a George Foster Peabody Award.

Block was recording an interview in Chengdu, China when the area was struck by a 7.9 magnitude earthquake. Her coverage of the earthquake earned NPR a George Foster Peabody Award.