For a deep geological repository for spent nuclear fuel planned in Sweden, the safety assessment covers up to 1 million years. Climate scenarios range from high-end global warming for the coming 100 000 years, through deep permafrost, to large ice sheets during glacial conditions. In contrast, in an existing repository for short-lived waste the activity decays to low levels within a few tens of thousands of years. The shorter assessment period, 100 000 years, requires more focus on climate development over the coming tens of thousands of years, including the earliest possibility for permafrost growth and freezing of the engineered system. The handling of climate and climate change in safety assessments must be tailor-made for each repository concept and waste type. However, due to the uncertain future climate development on these vast time scales, all safety assessments for nuclear waste repositories require a range of possible climate scenarios.