Enhancers are genomic DNA elements controlling spatiotemporal gene expression. Their flexible organization and functional redundancies make deciphering their sequence-function relationships challenging. This article provides an overview of the current understanding of enhancer organization and evolution, with an emphasis on factors that influence these relationships. Technological advancements, particularly in machine learning and synthetic biology, are discussed in light of how they provide new ways to understand this complexity. Exciting opportunities lie ahead as we continue to unravel the intricacies of enhancer function.Supplementary InformationThe online version contains supplementary material available at 10.1186/s13059-023-02955-4.