Animal genomes are compartmentalized into insulated regulatory units named topology-associated domains (TADs). TADs insulate gene promoters from enhancers that occupy neighboring TADs. Chromosomal rearrangements that disrupt TAD structure can generate new regulatory interactions between enhancers and promoters that were once separated into different TADs, which might lead to new gene expression patterns. On the one hand, TAD rearrangements are known to cause deleterious phenotypes, but, on the other hand, rearrangements can also create novel expression patterns that may be selected during evolution because they generate advantageous phenotypes. Here, we review recent studies that explore the effects of chromosomal rearrangements and genetic perturbations on TAD structure and gene regulation in the context of development and evolution. We discuss the possible contribution of evolutionary breakpoints (EBRs) that affect TAD structure to the evolution of gene regulation and the phenotype.