* 1982 Ledlie Prize, Harvard University
* 1988 Wallace P. Rowe Award, National Institute of Allergy and Infectious Diseases
* 1990 Louisa Gross Horwitz Prize (with Don Wiley and Michael Rossmann), Columbia University
* 1990 Harvey Lecturer, The Harvey Society, New York
* 1995 George Ledlie Prize, Harvard University
* 1997 ICN International Prize in Virology
* 2001 Paul Ehrlich and Ludwig Darmstaedter Prize (with Michael Rossmann)
* 2005 Bristol-Myers Squibb Award for Distinguished Achievement in Infectious Diseases Research
* 2006 Gregori Aminoff Prize in Crystallography (with David Stuart)
* 2007 UCSD/Merck Life Sciences Achievement Award
* 2011 William Silen Lifetime Achievement in Mentoring Award, Harvard Medical School
* 2012 Pauling Lectureship, Stanford University
* 2014 Elected as a Foreign Member of the Royal Society of London.
* 2015 The Welch Award in Chemistry
* 2015 Honorary Doctorate in Medicine, University of Milan
* 2018 48th Rosenstiel Award for research on proteins and viruses.