The repression of gene activity and the maintenance of the repressed state are fundamental requirements of cell differentiation, ordered embryonic development and tissue integrity. Furthermore, large regions of the genome such as centromeres and telomeres have a structural function and have to be kept transcriptionally inactive to be functional. In both cases the transcriptional silencing is accomplished through a dense packaging of the corresponding DNA into heterochromatin or heterochromatin-like structures. In this minireview we summarise recent findings, which point towards a major function of posttranslational histone modifications in the process of establishment and maintenance of condensed heterochromatin. The physical association of two enzymatic activities, histone methylation and histone deacetylation, which are thought to be involved in transcriptional silencing, provide the framework of a molecular model of how heterochromatin is initiated and maintained during cell division and differentiation.