Algorithmic governance as a key concept in controversies around the emerging digital society highlights the idea that digital technologies produce social ordering in a specific way. Starting with the origins of the concept, this paper portrays different perspectives and objects of inquiry where algorithmic governance has gained prominence ranging from the public sector to labour management and ordering digital communication. Recurrent controversies across all sectors such as datafication and surveillance, bias, agency and transparency indicate that the concept of algorithmic governance allows to bring objects of inquiry and research fields that had not been related before into a joint conversation. Short case studies on predictive policy and automated content moderation show that algorithmic governance is multiple, contingent and contested. It takes different forms in different contexts and jurisdictions, and it is shaped by interests, power, and resistance.