Organisms with the same genome can inherit information in addition to that encoded in the DNA sequence-this is known as epigenetic inheritance. Epigenetic inheritance is responsible for many of the phenotypic differences between different cell types in multicellular organisms. Work by many investigators over the past decades has suggested that a great deal of epigenetic information might be carried in the pattern of post-translational modifications of the histone proteins, although this is not as well established as many believe. For example, it is unclear whether and how the histones, which are displaced from the chromosome during passage of the replication fork and are often exchanged from the DNA template at other times, carry information from one cellular generation to the next. Here, we briefly review the evidence that some chromatin states are indeed heritable, and then focus on the mechanistic challenges that remain in order to understand how this inheritance can be achieved.