Chromatin modification is a fundamental mechanism of gene regulation in eukaryotes, but has not been duly included in the study of the evolution of gene regulation. In this talk, Ishall first explain the chromatin structure, the various types of chromatin modifications and their regulatory functions. Ishall then present our study on how chromatin structure may affect gene expression stability and therefore also the evolution of gene expression. Ishall then discuss the issue of how chromatin structure can be stably maintained in the midst of genetic and environmental changes. My colleagues and Ihave studied this issue using huge amounts of epigenetic data, transcription factor binding data, and gene expression data.We found that regions of the human genomethat maintain histone modifications among tissues tend to be conserved in the mouse genome as well. These evolutionarily and environmentally stable histone modifications often occur in regions of overlapped chromatin modifications, which coincide with clusters of TF binding events. Ishall discuss how TF binding events may increase the overlap and conservation of histone modifications.