In 1964, Haag and Kastler proposed a visionary framework for quantum field theory in which the algebraic relations between the observables take center stage. In a sense, the “operator product expansion”, proposed only some years later by Wilson, can be seen as one manifestation of their vision. It focusses directly on the unbounded quantum field theoretic operators typically of interest, rather than algebras of bounded operators as envisaged by Haag and Kastler. In this talk I report on important recent progress concerning this expansion, in particular on: The sense in which the operator product expansion describes an “algebra”, ways of computing the “structure constants” in the expansion, its status within conformal field theories and, as well as its convergence properties.