Summary: This is a republication of the paper “A Theorem on Petrov Types” [Acta Phys. Pol. 22, Suppl. 13–23 (1962; Zbl 0113.44807)] by J. Goldberg and R. Sachs, in which they proved the Goldberg-Sachs theorem. The article has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. Typographical errors of the original publication were corrected by the editor. The paper is accompanied by a Golden Oldie Editorial containing an editorial note written by A. Krasiński and M. Przanowski [Gen. Relativ. Gravitation 41, No. 2, 421–432 (2009; Zbl 1162.83317)] and Goldberg’s brief autobiography. The editorial note explains some difficult parts of the proof of the theorem and discusses the influence of results of the paper on later research.