Algorithmic management (AM) is reshaping work in many industries. However, what is done to redress potential risks is little understood. This study explores how trade unions, employers, and government actors assess AM-related occupational safety and health (OSH) risks and their strategies to understand how industrial relations could influence the safety and health of workers managed by digital technologies. Drawing on the Pressure, Disorganisation and Regulatory failure (PDR) model and interview and document data from Sweden, we find a gradually increasing interest in AM in the early 2020s among the government and the social partners. Unions learn, inform, and bargain about AM; employers enact ‘healthy discipline’; and government agencies inspect digital risks in workplaces. Moreover, economic and reward pressures contribute to AM-associated OSH risks. Disorganisation manifests as a lack of knowledge about the OSH effects of AM, leading to ineffective OSH management. Regulatory failure is reflected in new EU regulations stalling national-level initiatives, since the overlapping regulations complicate the enforcement of existing OSH regulations. This study highlights the crucial role of trade unions in advancing the agenda on AM-related OSH risks. It also makes a theoretical contribution by extending the PDR model, offering insights into the driving forces shaping AM and compromising OSH beyond the workplace level – highlighting wider politico-economic and institutional dynamics influencing OSH.