The two-disc live album Story Songs is based on the show of the same name that Buckley debuted at Joe's Pub at The Public Theater in September 2016.

The New York Times praised Story Songs as her "stunning new show, arguably the strongest of her career. Ms. Buckley, her voice in excellent shape, gave everything she sang the shape and depth of a personal confession."

When she took the program to the Bay Area later in the fall, she was called "a vocal wonder" by the San Francisco Chronicle.