Kaplansky made major contributions to group theory, ring theory, the theory of operator algebras and field theory and created the Kaplansky density theorem, Kaplansky's game and Kaplansky conjecture.
Kaplansky was the doctoral supervisor of 55 students including notable mathematicians Hyman Bass, Susanna S. Epp, Günter Lumer, Eben Matlis, Donald Ornstein, Ed Posner, Alex F. T. W. Rosenberg, Judith D. Sally, and Harold Widom.