Spatiotemporal gene expression programmes are orchestrated by transcriptional enhancers, which are key regulatory DNA elements that engage in physical contacts with their target-gene promoters, often bridging considerable genomic distances. Recent progress in genomics, genome editing and microscopy methodologies have enabled the genome-wide mapping of enhancer-promoter contacts and their functional dissection. In this Review, we discuss novel concepts on how enhancer-promoter interactions are established and maintained, how the 3D architecture of mammalian genomes both facilitates and constrains enhancer-promoter contacts, and the role they play in gene expression control during normal development and disease.