Eucalypts are the world's most widely planted hardwood trees. Their outstanding diversity, adaptability and growth have made them a global renewable resource of fibre and energy. We sequenced and assembled >94% of the 640-megabase genome of Eucalyptus grandis. Of 36,376 predicted protein-coding genes, 34% occur in tandem duplications, the largest proportion thus far in plant genomes. Eucalyptus also shows the highest diversity of genes for specialized metabolites such as terpenes that act as chemical defence and provide unique pharmaceutical oils. Genome sequencing of the E. grandis sister species E. globulus and a set of inbred E. grandis tree genomes reveals dynamic genome evolution and hotspots of inbreeding depression. The E. grandis genome is the first reference for the eudicot order Myrtales and is placed here sister to the eurosids. This resource expands our understanding of the unique biology of large woody perennials and provides a powerful tool to accelerate comparative biology, breeding and biotechnology.