Wright received the UN Correspondents Association Gold Medal for coverage of international affairs, the National Magazine Award for reportage from Iran in The New Yorker, and the Overseas Press Club Award for "best reporting in any medium requiring exceptional courage and initiative" for coverage of African wars. For coverage of US foreign policy, she was named journalist of the year by the American Academy of Diplomacy for "distinguished reporting and analysis of international affairs" and won the National Press Club Award and the Weintal Prize for diplomatic reporting. Wright has also been the recipient of a John D. and Catherine T. MacArthur Foundation grant.
Wright has been a fellow at the Carnegie Endowment for International Peace, the Brookings Institution, Yale University, Duke University, Stanford University, the University of California, Santa Barbara, and the University of Southern California. She also lectures extensively around the United States and has been a television commentator on ABC, NBC, CBS, CNN, and MSNBC programs, including Meet the Press, Face the Nation, This Week, Nightline, PBS NewsHour, Frontline, and Larry King Live.