Monitoring is now widely seen as a necessary part of programmes for the geological disposal of radioactive waste. However, we find different perspectives on the nature and role of monitoring. Among technical experts it is viewed firstly as a matter of performance confirmation, a tool for validating the safety case underlying repository construction. Among concerned citizens we find a view of monitoring as enabling the critical scrutiny of safety, an instrument for acknowledging uncertainties and detecting emergent problems in a repository. After outlining differing views on questions of whether, why, what, where and for how long to monitor we discuss monitoring in light of constant vigilance as a technical and moral principle of nuclear safety. We suggest that "how much monitoring" and "how should it be organised" are societal questions and as such need to be broadly discussed.