She subsequently developed an interest in classical voice and began studying with private instructors, and later with Edward Walker, vocal teacher at the University of Miami.

It was in Aix-en-Provence, with reedist and teacher Jean-François Bonnel [fr], that she studied improvisation, instrumental and vocal repertoire, and sang with her first band.

[11][12] In a four-star review of her sold-out engagement at Ronnie Scott's Club in London in June 2015, John Fordham wrote in The Guardian: "She brings ideas from unexpected angles to the familiar art of standards-singing, and she applies a mischievous intelligence to well-worn lyrics in ways that transform them.

[15] Salvant says that her main jazz influence is Sarah Vaughan, recalling childhood memories of listening to her songs repeatedly.

She enjoys popularity in Europe and in the United States, performing in clubs, concert halls, and festivals accompanied by renowned musicians.

Writing in The New York Times in 2012, Ben Ratliff said: "In front of a trio led by the pianist Aaron Diehl she sings clearly, with her full pitch range, from a pronounced low end to full and distinct high notes, used sparingly [...] Her voice clamps into each song, performing careful variations on pitch, stretching words but generally not scatting; her face conveys meaning, representing sorrow or serenity like a silent-movie actor.

[18] She has toured with the Jazz at Lincoln Center Orchestra, whose music director Wynton Marsalis was quoted in a 2017 New Yorker article as saying of Salvant: "You get a singer like this once in a generation or two.

The album, titled Mélusine, recounts the European folk legend of Melusine and largely features songs sung in French and Haitian Creole.