In the 1970's W. Nahm gave a classification of possible superconformal algebras, indicating that six is the maximum spacetime dimension for a superconformal field theory. Nevertheless, the first concrete evidence for an interacting 6D SCFT required input from string theory in the 1990's. In this talk we discuss a systematic approach to classifying all possible 6D superconformal field theories generated by backgrounds of F-theory. We also explain how the geometric description provides information on the physics of these theories.