Along with novel insights into the biology of individual sarcoma types, we report three overarching findings: (1) unlike most epithelial malignancies, these sarcomas (excepting synovial sarcoma) are characterized predominantly by copy-number changes, with low mutational loads and only a few genes (TP53, ATRX, RB1) highly recurrently mutated across sarcoma types; (2) within sarcoma types, genomic and regulomic diversity of driver pathways defines molecular subtypes associated with patient outcome; and (3) the immune microenvironment, inferred from DNA methylation and mRNA profiles, associates with outcome and may inform clinical trials of immune checkpoint inhibitors.