An art historian, a critic, and a curator, she has contributed articles and reviews to numerous journals—including Artforum, Art Journal, October, and Texte zur Kunst—as well as to exhibition catalogs for institutions throughout the world. Burton has curated or co-curated exhibitions including Sherrie Levine: Mayhem at the Whitney Museum of American Art, New York, in 2011 (with Elisabeth Sussman); Anti-Establishment at the Center for Curatorial Studies at Bard College, Annandale-on-Hudson, NY, in 2012; Take It or Leave It: Institution, Image, Ideology at the Hammer Museum, Los Angeles, in 2014 (with Anne Ellegood); and, at the New Museum, XFR STN in 2013; Wynne Greenwood: “Kelly” in 2015 (with Stephanie Snyder); Cheryl Donegan: “Scenes and Commercials” in 2016; Simone Leigh: “The Waiting Room” in 2016 (with Shaun Leonardo and Emily Mello); "A.K. Burns: Shabby But Thriving" in 2017 (with Sara O'Keeffe); and, most recently Trigger: Gender As A Tool And A Weapon (2017) among other projects.

She is the editor of Cindy Sherman (October Files, MIT Press, 2006); co-editor (with Shannon Jackson and Dominic Willsdon) of Public Servants: Art and the Crisis of the Common Good (New Museum and MIT Press, 2016); and co-editor (with Reina Gossett and Eric A. Stanley) of Trap Door: Trans Cultural Production and the Politics of Visibility (New Museum and MIT Press, 2017). Prior to her work at the New Museum, Burton was director of the graduate program at the Center for Curatorial Studies at Bard College (2010–2013) and associate director and senior faculty member at the Whitney Independent Study Program (2008–2010).