Gene expression studies in mammals and simpler eukaryotes have highlighted the central role that chromatin structure and modifications play in both the activation and repression of transcription. Aberrant chromatin structure can cause human genetic disease. Here we discuss recent progress in understanding the molecular mechanisms that underlie three human genetic diseases linked to perturbations of chromatin structure: ICF syndrome, facioscapulohumeral muscular dystrophy and a case of alpha-thalassaemia.