In 1981, Elizabeth Thompson was elected a member of the International Statistical Institute, and in 1988, she was awarded an Sc.D. degree by the University of Cambridge. In 1994, she gave the R.A.Fisher Lecture at the Joint Statistical Meetings in Toronto. In 1996, she gave the Neyman Lecture (IMS) at the Joint Statistical Meetings in Chicago. In 1998, she was elected a Fellow of the American Academy of Arts and Sciences. In 2001, she received the inaugural Jerome Sacks Award for Cross-Disciplinary Research from the National Institute for Statistical Science, and also the Weldon Prize for contributions to Biometry from the University of Oxford."

In 2002-3 Elizabeth Thompson held a Guggenheim Fellowship, and in 2006 (Nov-Dec), she was a Rothschild Visiting Professor at the Isaac Newton Institute, University of Cambridge . In 2008, she was elected to the US National Academy of Sciences, and in 2013 was elected an Honorary Fellow of Newnham College, Cambridge.

In recent years she has given several named lectures. In 2003 she was the Allen T. Craig Distinguished Lecturer at the University of Iowa, and in 2004 the Buehler-Martin Distinguished Lecturer at the University of Minnesota. In 2005 she was both the Mary Cartwright Lecturer at the London Mathematical Society, UK, and the Milton Sobel Lecturer at U. California Santa Barbara, and in 2006 was the Distinguished Lecturer in Statistical Science at the Fields Institute in Toronto, the Bahadur Lecturer at the University of Chicago, and gave the XXVII Fisher Memorial Lecture at the Isaac Newton Institute, in Cambridge, UK, In 2008, she gave the inaugural Tukey Lecture at the 7th World Congress in Probability and Statistics in Singapore, and the 2008 Kristnaiah Lecture at Penn State University. In 2009, she gave the 2008 Cockerham Lecture , NCSU; in 2012 the Woodroofe Lecture, University of Michigan; in 2015 the Rustagi Lecrure, Ohio State University.