In this article, we examine how human interactions with nuclear waste, with special regard to responsibilities and temporalities, have changed over time. Based primarily on historical and contemporary accounts, including interviews, we trace the history of how radioactive residue has been conceptualized and handled in Soviet and post-Soviet Russia and Sweden, from the Second World War to the present. By juxtaposing the practices and perspectives of dumping, management and care, our aim is to contribute to current efforts to make sense of waste in the Anthropocene. We conclude that to acknowledge a need for eternal care is to accentuate the interdependence of historical and geological temporalities.