Genetic studies promise to provide insight into the molecular mechanisms underlying type 2 diabetes (T2D). Variants associated with T2D are often located in tissue-specific enhancer regions (enhancer clusters, stretch enhancers or super-enhancers). So far, such domains have been defined through clustering of enhancers in linear genome maps rather than in 3D-space. Furthermore, their target genes are generally unknown. We have now created promoter capture Hi-C maps in human pancreatic islets. This linked diabetes-associated enhancers with their target genes, often located hundreds of kilobases away. It further revealed sets of islet enhancers, super-enhancers and active promoters that form 3D higher-order hubs, some of which show coordinated glucose-dependent activity. Hub genetic variants impact the heritability of insulin secretion, and help identify individuals in whom genetic variation of islet function is important for T2D. Human islet 3D chromatin architecture thus provides a framework for interpretation of T2D GWAS signals.