Towards the beginning of the 20th century, Sturdevant discovered that the genes of Drosophila are organized linearly on the chromosomes. Later, through hybridization experiments on polytene chromosomes, Sturdevant and Dobzhanski noticed that a substrand of the fruit fly DNA can be inverted; in some strains of fruit fly the sequence of genes on the chromosome appears in reverse order. Further, he showed that these
inversions were linked to the phenotype of those individuals that possessed it: male flies with a particular inversion had few or no male offspring. So as early as 1936, evolutionary histories between species of fruit fly were being inferred based on inversion histories. It is now known that rearrangements can both be fixed in a population,
and are associated with a multitude of diseases. It was not for another half a century that appropriate questions were asked about the inference of rearrangement histories. In this talk we introduce concepts and models for understanding rearrangement histories. We present our work relating 3D chromatin conformation, as represented by Hi-C data, to large-scale rearrangements across evolutionary time scales.