While population cycles are geographically widespread, it is on arctic tundra that such cycles appear to be most influential for the functioning of the whole ecosystem. We give an overview of tundra species that exhibit population cycles and describe what are currently believed to be the causal mechanisms. Population cycles most likely originate from trophic interactions within the plant-based tundra food web, where lemmings, either as prey for carnivores or as consumers of plants, play the key role. The predominance of trophic interaction cycles at northern latitudes is ultimately related to climate, and such cycles should therefore be vulnerable to climate change. Recent evidence indicates that changes have already taken place in the dynamics of some key herbivores and their predators, consistent with the expected impacts of climate change. There is a strong need for large-scale integrated monitoring and research efforts to further document such changes and their ecosystem consequences.