Smalley, the youngest of 4 siblings, was born in Akron, Ohio on June 6, 1943 to Frank Dudley Smalley, Jr., and Esther Virginia Rhoads. He grew up in Kansas City, Missouri. Richard Smalley credits his Father, mother and aunt as formative influences in industry, science and chemistry. His Father, Frank Dudley Smalley, Jr. worked with mechanical and electrical equipment and eventually became CEO of a trade journal for farm implements called Implement and Tractor. His mother, Esther Rhoads Smalley, completed her B.A. Degree while Richard was a teenager. She was particularly inspired by Mathematician Norman N. Royall Jr., who taught Foundations of Physical Science, and communicated her love of science to her son through long conversations and joint activities. Smalley's mother's sister, pioneering woman Chemist Sara Jane Rhoads, interested Smalley in the field of chemistry, letting him work in her organic chemistry laboratory, and suggesting that he attend Hope College, which had a strong chemistry program.

Smalley attended Hope College for two years before transferring to the University of Michigan where he received his Bachelor of Science in 1965. Between his studies, he worked in industry, where he developed his unique managerial style. He received his Doctor of Philosophy (Ph.D.) from Princeton University in 1973 with Prof. E. R. Bernstein. He did postdoctoral work at the University of Chicago from 1973 to 1976, with Donald Levy and Lennard Wharton where he was a pioneer in the development of supersonic beam laser spectroscopy.

Smalley was married four times, to Judith Grace Sampieri (1968-1978), Mary L. Chapieski (1980-1994), JoNell M. Chauvin (1997-1998) and Deborah Sheffield (2005), and had two sons, Chad Richard Smalley (born June 8, 1969) and Preston Reed Smalley (born August 8, 1997).

In 1976, Smalley joined Rice University. In 1982, he was appointed to the Gene and Norman Hackerman Chair in Chemistry at Rice. He helped to found the Rice Quantum Institute in 1979, serving as Chairman from 1986 to 1996. In 1990, he became also a Professor in the Department of Physics. In 1990, he helped to found the Center for Nanoscale Science and Technology. In 1996, he was appointed its Director.

This research is significant for the discovery of a new allotrope of carbon known as a fullerene. Other allotropes of carbon include graphite, Diamond and graphene. Harry Kroto's 1985 paper entitled "C60: Buckminsterfullerine", published with colleagues J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, was honored by a Citation for Chemical Breakthrough Award from the Division of History of Chemistry of the American Chemical Society, presented to Rice University in 2015. The discovery of fullerenes was recognized in 2010 by the designation of a National Historic Chemical Landmark by the American Chemical Society at the Richard E. Smalley Institute for Nanoscale Science and Technology at Rice University in Houston, Texas.

Starting in the late 1990s, Smalley advocated for the need for cheap, clean Energy, which he described as the number one Problem facing humanity in the 21st century. He described what he called "The Terawatt Challenge", the need to develop a new power source capable of increasing "our Energy output by a minimum factor of two, the generally agreed-upon number, certainly by the middle of the century, but preferably well before that."

Smalley was a leading advocate of the National Nanotechnology Initiative in 2003. Suffering from hair loss and weakness as a result of his chemotherapy treatments, Smalley testified before the congressional testimonies, arguing for the potential benefits of nanotechnology in the development of targeted cancer therapies. Bill 189, the 21st Century Nanotechnology Research and Development Act, was introduced in the Senate on January 16, 2003 by Senator Ron Wyden, passed the Senate on November 18, 2003, and at the House of Representatives the next day with a 405–19 vote. President George W. Bush signed the act into law on December 3, 2003, as Public Law 108- 153. Smalley was invited to attend.

He also presented a list entitled "Top Ten Problems of Humanity for Next 50 Years". It can be interesting to compare his list, in order of priority, to the Ten Threats formulated by the U.N.'s High Level Threat Panel in 2004. Smalley's list, in order of priority, was:

At the Tuskegee University's 79th Annual Scholarship Convocation/Parents' Recognition Program he was quoted making the following statement regarding the subject of evolution while urging his audience to take seriously their role as the higher species on this planet. "'Genesis' was right, and there was a creation, and that Creator is still involved... We are the only species that can destroy the Earth or take care of it and nurture all that live on this very special planet. I'm urging you to look on these things. For whatever reason, this planet was built specifically for us. Working on this planet is an absolute moral code. ... Let's go out and do what we were put on Earth to do." Old Earth creationist and Astronomer Hugh Ross spoke at Smalley's funeral, November 2, 2005.

He was an outspoken skeptic of the idea of molecular assemblers, as advocated by K. Eric Drexler. His main scientific objections, which he termed the “fat fingers problem" and the "sticky fingers problem”, argued against the feasibility of molecular assemblers being able to precisely select and place individual atoms. He also believed that Drexler’s speculations about apocalyptic dangers of molecular assemblers threatened the public support for development of nanotechnology. He debated Drexler in an exchange of letters which were published in Chemical & Engineering News as a point-counterpoint feature.