1960-62
Alfred P. Sloan Research Fellowship
1964- 
Foreign Membership, Brazilian Academy of Science 
1965
Veblen Prize, American Mathematical Society 
1966
Fields Medal, International Mathematical Union 
1967 
University of Michigan Sesquicentennial Award 
1967-
Membership, American Academy of Arts and Sciences 
1967-68, 79-80, 90
Research Professorship Miller Institute for Basic Research in Science, Berkeley 
1970-
Membership, National Academy of Sciences 
1972
Colloquium Lectureship, American Mathematical Society 
1974
Honorary D. Sc., University of Warwick, England
1983- 
Election as Fellow, The Econometric Society 
1983
Faculty Research Lectureship, University of California, Berkeley 
1987
Honorary D. Sc., Queens University, Kingston, Ontario 
1988
Chauvenet Prize, Mathematical Association of America
1989
Von Neumann Award, Society for Industrial and Applied Mathematics 
1990
Honorary Membership in Instituto de Mathematics Pura ed Aplicada (IMPA) Rio de Janeiro 
1993
Fellow of the Japan Society for the Promotion of Science 
1994
Class of the Grand Cross of the Brasilian National Order of Scientific Merit 
1996
Honorary Doctor of Science, University of Michigan
National Medal of Science, Washington, D.C. 
1997
Doctor Honoris Causa, Universite Pierre et Marie Curie, Paris 
1997
Honorary Doctor of Science, City Univerisity of Hong Kong 
1997
Honorary Professor, University of Yunnan, Kunming 
Honorary Member of the Moscow Mathematical Society 
1998
Honorary Member of the London Mathematical Society 
1999
Honorary Doctorate of Rostov State University 
2000
Crimean Astrophysical Observatory and Institute of Applied Astronomy of Russian Academy of Science named a newly discovered minor planet "Smale Planet" 

2006

Wolf Prize, International Mathematical Union