The extinction of species of small invertebrates is difficult to recognize. However, in deposits that date from the past few million years, insect fossils are remarkably common and provide objective data on the history of the organisms that constitute the biotic communities of the present day. It might have been expected that the great climatic oscillations of the glacial-interglacial cycles should have caused widespread extinctions, if their effects on the large vertebrates is taken as our model. Yet the record of Quaternary fossil insects shows no high extinction rates during this period. Constancy of species and communities of species can be demonstrated to be the norm for at least the last million or so years (= generations). The enigma of how such constancy was sustained in the face of large-scale climatic fluctuations remains a puzzle though several possible solutions are suggested. These solutions carry implications for our estimates of present and future extinction rates.