The division of the genome into discrete chromosomes is a fundamental characteristic of eukaryotic life. Insect taxonomists’ early adoption of cytogenetics has led to an incredible amount of data describing genome structure across insects. In this article, we synthesize data from thousands of species and use biologically realistic models to infer the tempo and mode of chromosome evolution among insect orders. Our results show that orders vary dramatically in the overall rate of chromosome number evolution (a proxy of genome structural stability) and the pattern of evolution (e.g., the balance between fusions and fissions). These findings have important implications for our understanding of likely modes of speciation and offer insight into the most informative clades for future genome sequencing.