Insects are among the most diverse and widespread animals across the biosphere and are well-known for their contributions to ecosystem functioning and services. Recent increases in the frequency and magnitude of climatic extremes (CE), in particular temperature extremes (TE) owing to anthropogenic climate change, are exposing insect populations and communities to unprecedented stresses. However, a major problem in understanding insect responses to TE is that they are still highly unpredictable both spatially and temporally, which reduces frequency- or direction-dependent selective responses by insects. Moreover, how species interactions and community structure may change in response to stresses imposed by TE is still poorly understood. Here we provide an overview of how terrestrial insects respond to TE by integrating their organismal physiology, multitrophic, and community-level interactions, and building that up to explore scenarios for population explosions and crashes that have ecosystem-level consequences. We argue that TE can push insect herbivores and their natural enemies to and even beyond their adaptive limits, which may differ among species intimately involved in trophic interactions, leading to phenological disruptions and the structural reorganization of food webs. TE may ultimately lead to outbreak–breakdown cycles in insect communities with detrimental consequences for ecosystem functioning and resilience. Lastly, we suggest new research lines that will help achieve a better understanding of insect and community responses to a wide range of CE.