Tasmanian devils have spawned two transmissible cancer lineages, named devil facial tumor 1 (DFT1) and devil facial tumor 2 (DFT2). We investigated the genetic diversity and evolution of these clones by analyzing 78 DFT1 and 41 DFT2 genomes relative to a newly assembled, chromosome-level reference. Time-resolved phylogenetic trees reveal that DFT1 first emerged in 1986 (1982 to 1989) and DFT2 in 2011 (2009 to 2012). Subclone analysis documents transmission of heterogeneous cell populations. DFT2 has faster mutation rates than DFT1 across all variant classes, including substitutions, indels, rearrangements, transposable element insertions, and copy number alterations, and we identify a hypermutated DFT1 lineage with defective DNA mismatch repair. Several loci show plausible evidence of positive selection in DFT1 or DFT2, including loss of chromosome Y and inactivation of MGA, but none are common to both cancers. This study reveals the parallel long-term evolution of two transmissible cancers inhabiting a common niche in Tasmanian devils.