Heterochromatin is composed of tightly condensed chromatin in which the histones are deacetylated and methylated, and specific nonhistone proteins are bound. Additionally, in vertebrates and plants, the DNA within heterochromatin is methylated. As the heterochromatic state is stably inherited, replication of heterochromatin requires not only duplication of the DNA but also a reinstallment of the appropriate protein and DNA modifications. Thus replication of heterochromatin provides a framework for understanding mechanisms of epigenetic inheritance. In recent studies, roles have been identified for replication factors in reinstating heterochromatin, particularly functions for origin recognition complex, proliferating cell nuclear antigen, and chromatin-assembly factor 1 in recruiting the heterochromatin binding protein HP1, a histone methyltransferase, a DNA methyltransferase, and a chromatin remodeling complex. Potential mechanistic links between these factors are discussed. In some cells, replication of the heterochromatin is blocked, and in Drosophila this inhibition is mediated by a chromatin binding protein SuUR.