Topologically associating domains, or TADs, are functional units that organize chromosomes into 3D structures of interacting chromatin. TADs play an important role in regulating gene expression by constraining enhancer-promoter contacts and there is evidence that deletion of TAD boundaries leads to aberrant expression of neighboring genes. While the mechanisms of TAD formation have been well-studied, current knowledge on the patterns of TAD evolution across species is limited. Due to the integral role TADs play in gene regulation, their structure and organization is expected to be conserved during evolution. However, more recent research suggests that TAD structures diverge relatively rapidly. We use Hi-C chromosome conformation capture to measure evolutionary conservation of whole TADs and TAD boundary elements between D. melanogaster and D. triauraria, two early-branching species from the melanogaster species group which diverged ∼15 million years ago. We find that the majority of TADs have been reorganized since the common ancestor of D. melanogaster and D. triauraria, via a combination of chromosomal rearrangements and gain/loss of TAD boundaries. TAD reorganization between these two species is associated with a localized effect on gene expression, near the site of disruption. By separating TADs into subtypes based on their chromatin state, we find that different subtypes are evolving under different evolutionary forces. TADs enriched for broadly expressed, transcriptionally active genes are evolving rapidly, potentially due to positive selection, whereas TADs enriched for developmentally-regulated genes remain conserved, presumably due to their importance in restricting gene-regulatory element interactions. These results provide novel insight into the evolutionary dynamics of TADs and help to reconcile contradictory reports related to the evolutionary conservation of TADs and whether changes in TAD structure affect gene expression.