Miscanthus is a perennial wild grass that is of global importance for paper production, roofing, horticultural plantings, and an emerging highly productive temperate biomass crop. We report a chromosome-scale assembly of the paleotetraploid M. sinensis genome, providing a resource for Miscanthus that links its chromosomes to the related diploid Sorghum and complex polyploid sugarcanes. The asymmetric distribution of transposons across the two homoeologous subgenomes proves Miscanthus paleo-allotetraploidy and identifies several balanced reciprocal homoeologous exchanges. Analysis of M. sinensis and M. sacchariflorus populations demonstrates extensive interspecific admixture and hybridization, and documents the origin of the highly productive triploid bioenergy crop M. × giganteus. Transcriptional profiling of leaves, stem, and rhizomes over growing seasons provides insight into rhizome development and nutrient recycling, processes critical for sustainable biomass accumulation in a perennial temperate grass. The Miscanthus genome expands the power of comparative genomics to understand traits of importance to Andropogoneae grasses.