Initially W. E. Story was associate editor in charge; he was replaced by Thomas Craig in 1880.

For volume 7 Simon Newcomb became chief editor with Craig managing until 1894.

Then with volume 16 it was "Edited by Thomas Craig with the Co-operation of Simon Newcomb" until 1898.

[2] Other notable mathematicians who have served as editors or editorial associates of the journal include Frank Morley, Oscar Zariski, Lars Ahlfors, Hermann Weyl, Wei-Liang Chow, S. S. Chern, André Weil, Harish-Chandra, Jean Dieudonné, Henri Cartan, Stephen Smale, Jun-Ichi Igusa, and Joseph A. Shalika.

Fields medalist Cédric Villani has speculated that "the most famous article in its long history" may be a 1958 paper by John Nash, "Continuity of solutions of parabolic and elliptic equations".