In the cereal crop sorghum (Sorghum bicolor) inflorescence morphology variation underlies yield variation and confers adaptation across precipitation gradients, but its genetic basis is poorly understood. We characterized the genetic architecture of sorghum inflorescence morphology using a global nested association mapping (NAM) population (2200 recombinant inbred lines) and 198,000 phenotypic observations from multi-environment trials for four inflorescence morphology traits (upper branch length, lower branch length, rachis length, and rachis diameter). Trait correlations suggest that lower and upper branch length are under somewhat independent control, while lower branch length and rachis diameter are highly pleiotropic. Joint linkage and genome-wide association mapping revealed an oligogenic architecture with 1-22 QTL per trait, each explaining 0.1-5.0% of variation across the entire NAM population. There is a significant enrichment (2.twofold) of QTL colocalizing with grass inflorescence gene homologs, notably with orthologs of maize Ramosa2 and rice Aberrant Panicle Organization1 and TAWAWA1. Still, many QTL do not colocalize with inflorescence gene homologs. In global georeferenced germplasm, allelic variation at the major inflorescence QTL is geographically patterned but only weakly associated with the gradient of annual precipitation. Comparison of NAM with diversity panel association suggests that naive association models may capture some true associations not identified by mixed linear models. Overall, the findings suggest that global inflorescence diversity in sorghum is largely controlled by oligogenic, epistatic, and pleiotropic variation in ancestral regulatory networks. The findings also provide a basis for genomics-enabled breeding of locally-adapted inflorescence morphology.