* 1974 – National Fresenius Award, Phi Lambda Upsilon
* 1976 – Member, National Academy of Sciences
* 1976 – Member, American Academy of Arts and Sciences
* 1979 – inaugural recipient of the Michael Polanyi Medal, Royal Society of Chemistry
* 1981 – Earle K. Plyler Prize
* 1983 – Spectroscopy Society of Pittsburgh Award
* 1983 – National Medal of Science
* 1985 – Irving Langmuir Award in Chemical Physics
* 1986 – Michelson-Morley Award
* 1986 – John Gamble Kirkwood Award, ACS New Haven Section, "in recognition of his fundamental contributions in experimental and theoretical aspects of reaction dynamics."
* 1990 – Willard Gibbs Medal
* 1991 – Peter Debye Award
* 1991 – National Academy of Sciences Award in Chemical Sciences, "For his pioneering laser-based techniques, deep insights, and seminal contributions, which have influenced every facet of chemical reaction dynamics."
* 1991 – Member, American Philosophical Society
* 1993 – Dannie Heineman Prize
* 1993 – The Harvey Prize
* 1995 – ACS Division of Analytical Chemistry Award in Chemical Instrumentation
* 1996 – The Bing Fellowship teaching award
* 1997 – California Scientist of the Year Award
* 1998 – American Chemical Society Award in Analytical Chemistry
* 1999 – E. Bright Wilson Award in Spectroscopy
* 1999 – Welch Award in Chemistry
* 1999 – Foreign Member of the Royal Society of London
* 2000 – honorary doctorate, Faculty of Science and Technology, Uppsala University, Sweden
* 2000 – Arthur L. Schawlow Prize in Laser Science
* 2000 – Nobel Laureate Signature Award for Graduate Education
* 2001 – Charles Lathrop Parsons Award
* 2001 – Faraday Lectureship Prize, Royal Society of Chemistry
* 2003 – Laurance and Naomi Carpenter Hoagland Prize
* 2004 – Foreign member, Royal Swedish Academy of Sciences
* 2004 – Foreign member, Chinese Academy of Sciences (CAS), Beijing, P.R.C.
* 2004 – James Flack Norris Award for Outstanding Achievement in the Teaching of Chemistry, Northeastern Section of the American Chemical Society
* 2005 – Nichols Medal, ACS (New York Section) 
* 2005 – Wolf Prize in Chemistry
* 2005 – Howard Hughes Medical Institute Professorship
* 2009 – F.A. Cotton Medal for Excellence in Chemical Research of the American Chemical Society
* 2009 – BBVA Foundation Frontiers of Knowledge Award in Basic Science (co-winner with Michael Fisher)
* 2010 – Priestley Medal
* 2011 – King Faisal International Prize
*2012 – Recipient of the Reed M. Izatt and James J. Christensen Lectureship.
*2017 – Othmer Gold Medal from the Chemical Heritage Foundation