Organizing scholarly publishing as a cooperative business has the promise of making journals more affordable and scholarly publishing more sustainable. The authors describe the development of the modern cooperative from its beginnings in England during the Industrial Revolution and highlight the great extent and diversity of business worldwide that is currently done cooperatively. Some of the current initiatives in scholarly publishing (SPARC, PLoS, German Academic Publishing, etc.) are analysed in light of cooperative business principles, and it is shown that, while these models often partially utilize cooperative business practices, none of them has adopted the cooperative model in totality.