From 1990 to 2002 Storr was curator, then senior curator, in the Department of Painting and Sculpture at the Museum of Modern Art. As a curator, Storr made his mark early with a number of major exhibitions at the museum and elsewhere, which enhanced the public prominence of such artists as Elizabeth Murray, Gerhard Richter, Max Beckmann, Tony Smith and Robert Ryman. He also organized a number of reinstallations of MoMA's permanent collection, covering such topics as abstraction and the modern grotesque. From 2002 to 2006 he was the first Rosalie Solow Professor of Modern Art at the Institute of Fine Arts, New York University. Per New York magazine, he is considered to be one of the most influential Americans in the art world.
Storr has been described as "an artist who's logged enough studio time to have a special regard for painters' painters ... and a gifted writer who can make us appreciate them, too." and a "vital link between the museum world and academia."
Over the years, he has written for the following publications: Art in America, Artforum, Art Press, Frieze, New York Times, Washington Post, Village Voice, The Brooklyn Rail, Art & Design, and Interview. Until April 2011 his regular column 'View from the Bridge' appeared in Frieze magazine.
He was the first American commissioner of the Venice Biennale in 2007. He has taught at the CUNY graduate center and the Bard Center for Curatorial Studies as well as the Rhode Island School of Design, Tyler School of Art, New York Studio School and Harvard University, and has been a frequent lecturer in this country and abroad. Storr was reappointed Dean of the Yale School of Art for a second five-year period beginning July 2011. After completing his second term as Dean, Storr continues to teach at the Yale School of Art as a tenured Professor in the Department of Painting/Printmaking. 
Awards and honors
He has been awarded a Penny McCall Foundation Grant for painting, a Norton Family Foundation Curator Grant, a Guggenheim Fellowship in 2016, and honorary doctorates from the School of the Art Institute of Chicago, the Maine College of Art, Swarthmore College, the University of the Arts London, and Montserrat College of Art. He also received awards from the American Chapter of the International Association of Art Critics, a special AICA award for Distinguished Contribution to the Field of Art Criticism, an ICI Agnes Gund Curatorial Award, and the Lawrence A. Fleischman Award for Scholarly Excellence in the Field of American Art History from the Smithsonian Institution's Archives of American Art. In June 2017 his book, "Intimate Geometries: The Art and Life of Louise Bourgeois" was awarded the FILAF D'OR at the Festival International du Livre d'Art et du Film, Pergignan, France. In 2000 the French Ministry of Culture presented him with the medal of Chevalier des Arts et des Lettres and in 2010 promoted him to Officier of the same order.
Storr's published writings encompass 290 works in 390 publications in 12 languages and 18,002 library holdings.
- Philip Guston: A Life Spent Painting, Laurence King Publishing, 2020
- Robert Storr Interviste sull'arte, edited and with a preface by Francesca Pietropaolo, 2019 (in Italian)
- Unfettering Reveries: The Incompiuto Siciliano. In Robert Storr, Marc Auge, Alterazioni Video et al. Incompiuto. The Birth of a Style. Milan: Humboldt Books, 2018
- Robert Storr Interviews on Art, edited and with a preface by Francesca Pietropaolo, 2017
- Intimate Geometries: the Art and Life of Louise Bourgeois, 2016
- How to Look: Ad Reinhardt Art Comics, 2013
- Selections from the private collection of Robert Rauschenberg, 2012
- In direzione ostinata e contraria: scritti sull'arte contemporanea,, edited, introduced and translated by Francesca Pietropaolo 2011
- The Painter's Painter essay in Arshille Gorky: A Retrospective, 2010
- September: A History Painting by Gerhardt Richter, 2009
- Gerhardt Richter: the Cage Paintings, 2009
- Think with the senses, feel with the mind: art in the present tense, 2007
- Concentration Now Begins... essay in Thomas Nozkowski; Subject to Change, 2007
- As Far as the Eye Can See essay in Rackstraw Downes, 2005
- Elizabeth Murray, 2005
- Popped Art, 2005
- Touching Down Lightly, 2005
- Disparities & Deformations: Our Grotesque, 2004
- Louise Bourgeois, 2003
- Gerhard Richter: Doubt and Belief in Painting, 2003
- Nancy Spero : The War Series, 1966-1970, 2003
- Gerhard Richter: Forty Years of Painting, 2002
- Philip Pearlstein Since 1983, 2002
- Modern Art Despite Modernism, 2000
- Gerhard Richter : October 18, 1977, 2000
- Prince of Tides : Robert Storr talks with Harald Szeemann, 1999
- On the Edge : Contemporary Art from the Werner and Elaine Dannheisser collection, 1998
- Chuck Close, 1998
- Franz West, 1997
- Bruce Nauman, 1995
- Between a Rock and a Hard Place, 1994
- Mapping, 1994
- Robert Ryman, 1993
- Devil on the Stairs: Looking Back on the Eighties, 1991
- Dislocations, 1991
- Art, censorship and the First Amendment: this is not a test, 1991
- Philip Guston, 1986
- Tilted Arc: Enemy of the People?, 1985
- 'Three to Receive Honorary Degrees at Commencement 2008', Swarthmore College News and Information, undated. Retrieved 18 May 2008.
- 'The Most Influential Americans in Art' Archived 2008-07-20 at the Wayback Machine, New York Magazine, 7 May 2006. Retrieved 6 December 2007.
- "Archived copy". Archived from the original on 2008-07-20. Retrieved 2014-04-09.CS1 maint: archived copy as title (link)
- 'Yale University press release', undated. Retrieved 6 December 2007.
- International Foundation for Art Research, about IFAR
- WorldCat Identities: Robert Storr
- Form/Space Atelier Exhibits Robert Storr's Autograph And Other Work 
- Watch Chuck Close and Robert Storr in Conversation on BUniverse
- Venice Bienniale website, English version.
- "The Most Influential Americans in Art", in New York magazine, accessed 5 October 2006.
- "Critic, artist and curator Robert Storr named Dean of the Yale School of Art". Yale University press release, February 28, 2006.
- Watch Robert Storr presenting his book Interviste sull'arte at Accademia di San Luca, Rome, May 17, 2019 (in English and Italian): https://www.youtube.com/watch?v=k037nOnh9KI
- Watch Robert Storr moderating the panel "Visions of Nature in the Age of Climate Change", Chiesa delle Penitenti, Venice, May 11-12, 2019 (as part of the public program of a Collateral Event of the 2019 Venice Biennale): https://www.youtube.com/watch?v=m9SdrhNDoT8&mc_cid=1209079652&mc_eid=ccae586ff2