Histones are important component of eukaryotic cells chromatin and consist of arginine and lysine residues. Histones play an important role in the protection of DNA. Their contents significantly affect high-level chromatin structure formation, gene expression, DNA replication, and other important life activities. Protein degradation is an important regulatory mechanism of histone content. Recent studies have revealed that modification of amino acid sequence is directly related to histone breakdown. In addition, histone degradation is closely related to covalent modifications, such as ubiquitination and acetylation, which are considered to be driving factors in gene regulation. Gene regulation is an important mechanism in adaptation to the environment and survival of species. With the introduction of highly efficient technology, various mutations in histones have been identified in yeast. In the field of epigenetics and the transmission of chromatin states, two widely used model organisms are the budding yeast Saccharomyces cerevisiae and Schizosaccharomyces pombe. Higher eukaryotes can use their silent loci to maintain their epigenetic states and providing the base to investigate mechanisms underlying development. Therfore, both species have contributed a plethora of information on these mechanisms in both yeast and higher eukaryotes. This study focuses on the role of histone modifications in controlling telomeric silencing in Saccharomyces cerevisiae and centromeric silencing in S. pombe as examples of genetic loci that demonstrate epigenetic inheritance. In view of recent advances, this review focuses on the post-translational modification of histone amino acid residues and reviews the relationship between histone degradation and amino acid residue modification.