Wilson was educated at Harvard and Cal Tech where he gained his PhD in 1969. He taught at Cornell University from 1963, serving as professor of physics there from 1970 to 1988, when he moved to a similar post at Ohio State University, Columbus.

Wilson received the 1982 Nobel Prize for physics for theoretical work on critical phenomena in connection with phase transitions. He first applied his methods to the problem of ferromagnetic materials. Above a certain temperature, known as the Curie point, such materials become paramagnetic. This behavior results from the individual magnetic moments of the atoms. In the ferromagnetic state numbers of individual atoms ‘couple’ together so that their spins are aligned, and there is a resulting long-range interaction over a region of the solid. Above the critical point (the Curie point) this long-range order breaks down. Wilson's achievement was to develop a theory that could apply to the system near the critical point.

He did this using an idea first suggested by Leo Kadanoff (1937–2015). He took a block of atoms and calculated the effective spin of the block, then took a number of blocks and calculated the value for the larger block, and so on. The method involves a mathematical technique known as renormalization.

Using such methods Wilson could go from the properties of individual atoms to properties characteristic of many atoms acting together, and the resulting theory could be applied to properties other than magnetism. Thus it can be used for the critical state observed in the change between liquid and gas and to changes in alloy structure. Wilson then applied his methods to the strong forces between nucleons.