Jennings is Professor Emeritus in the Department of Civil Engineering and Applied Mechanics, California Institute of Technology. He served as executive officer for Civil Engineering and Applied Mechanics, and as Chairman of the Division of Engineering and Applied Science from 1985 to 1989. He was Caltech's Vice President and Provost between 1989-95, and later served twice as Acting Vice President for Business and Finance. He was a member of the Board of Directors of Enresco, Inc., in Colorado Springs and served two years on the Teaching Staff at the US Air Force Academy, Department of Mechanics.

Jennings served as a member of the California Council on Science and Technology from 1995-2002, including a term as chair of the Council. He is a member of the National Academy of Engineering, past President of the Seismological Society of America, and past President of the Earthquake Engineering Research Institute. He is the author of numerous technical papers on earthquake engineering and dynamics of structures and has served as earthquake engineering consultant on the design of high-rise buildings, offshore drilling towers, nuclear power plants, and other major projects. A member of ASCE, he is past Chairman of the Executive Committee of the Engineering Mechanics Division and served a term as chairman of the Structural Dynamics Committee. He has studied earthquake damage in various parts of the world and was co-editor of the Engineering Volume of the National Academy of Sciences report on the great Alaska earthquake of 1964.

He was a member of the Board of Inquiry on the Loma Prieta earthquake appointed by Governor Deukmejian and is chair of the City Hall Oversight Committee for the seismic rehabilitation of Pasadena City Hall. He has received the Newmark Medal, the Huber Prize of the American Society of Civil Engineers, and the Honor Alumnus and the Achievement in Academic Awards from his undergraduate alma mater, Colorado State University. He is a member of the American Society of Civil Engineers, the Seismological Society of America, the Structural Engineers Association of California, the American Geophysical Union, and the American Society for Engineering Education.