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Gladstone has covered media for much of her career. In the early 1980s, she covered public broadcasting for the industry newspaper Current and reported for Cablevision and The Washington Weekly, in Washington, D.C.

In 1987, at the age of 32, she joined National Public Radio, first as editor of Weekend Edition with Scott Simon, and then as senior editor of All Things Considered. In 1991, she received a Knight Fellowship to study Russian language and history. A year later, she was reporting from Moscow for NPR, covering stories such as the bloody 1993 power struggle. In 1995, Gladstone returned to the United States and was hired as NPR's first "media reporter," based in New York City.

In 2019, Gladstone joined NPR Detroit to host a one month long series on the house evictions crisis on Detroit today with Stephen Henderson.