This authoritative text/reference presents a review of the history, current status, and potential future directions of computational biology in molecular evolution. Gathering together the unique insights of an international selection of prestigious researchers, this must-read volume examines the latest developments in the field, the challenges that remain, and the new avenues emerging from the growing influx of sequence data. These viewpoints build upon the pioneering work of David Sankoff, one of the founding fathers of computational biology, and mark the 50th anniversary of his first scientific article. Topics and features: Discusses the development of the BLAST algorithm, model-based phylogeography techniques, and the double cut and join (DCJ) distance formula Reviews the reconstruction of evolutionary features of ancestral genomes in a known phylogeny, and presents integrative models of evolution Introduces algorithms to estimate alignment and phylogeny on ultra-large datasets, and an approach for using likelihood methods with rearrangement models Examines the impact of insertion and deletion variants in human biology, evolution and health Surveys novel and recent research on genomic distance and family-free genome comparison Describes consolidation methods for reconstruction of ancestral gene orders, and error detection in gene tree construction Investigates  the genetic events recoverable from simulations of human population histories The broad spectrum of rich contributions in this essential collection will appeal to all computer scientists, mathematicians and biologists involved in comparative genomics, phylogenetics and related areas.