Peters was the Students’ Visiting Lecturers Trust Fund Lecturer at the University of Natal in Pietermaritzburg, South Africa, in 1975 and was a visiting fellow of the Japan Society for the Promotion of Science in 1980. In 2006, he was recognized for his 50-year membership in the American Chemical Society, and in 2007 he was elected a fellow of The Electrochemical Society.
At IU, Peters received a Distinguished Service Award in 2005, the W. George Pinnell Award for Outstanding Service in 2006, and the College's inaugural Career Teaching Award in 2018. Throughout his five-decade career in Bloomington, Peters has also received 11 teaching awards from the university. He is the coauthor of five undergraduate textbooks on analytical chemistry and has served the chemistry department as associate chair, graduate advisor, director of general chemistry, coordinator of undergraduate studies, and advisor for graduate students in the Master of Arts for Teachers program.