The study of chromosome evolution is undergoing a resurgence of interest owing to advances in DNA sequencing technology that facilitate the production of chromosome-scale whole-genome assemblies de novo. This review focuses on the history, methods, discoveries, and current challenges facing the field, with an emphasis on vertebrate genomes. A detailed examination of the literature on the biology of chromosome rearrangements is presented, specifically the relationship between chromosome rearrangements and phenotypic evolution, adaptation, and speciation. A critical review of the methods for identifying, characterizing, and visualizing chromosome rearrangements and computationally reconstructing ancestral karyotypes is presented. We conclude by looking to the future, identifying the enormous technical and scientific challenges presented by the accumulation of hundreds and eventually thousands of chromosome-scale assemblies.