Genetic variation associated with disease often appears in non-coding parts of the genome. Understanding the mechanisms by which this phenomenon leads to disease is necessary to translate results from genetic association studies to the clinic. Assigning function to this type of variation is notoriously difficult because the human genome harbours a complex regulatory landscape with a dizzying array of transcriptional regulatory sequences, such as enhancers that have unpredictable, promiscuous and context-dependent behaviour. In this Review, we discuss how technological advances have provided increasingly detailed information on genome folding; for example, genome folding forms loops that bring enhancers and target genes into close proximity. We also now know that enhancers function within topologically associated domains, which are structural and functional units of chromosomes. Studying disease-associated mutations and chromosomal rearrangements in the context of the 3D genome will enable the identification of dysregulated target genes and aid the progression from descriptive genetic association results to discovering molecular mechanisms underlying disease.