Two problems related to the biological identity of living beings are faced: the who-problem (which are the biological properties making that living being unique and different from the others?); the persistence-problem (what does it take for a living being to persist from a time to another?). They are discussed inside a molecular biology framework, which shows how epigenetics can be a good ground to provide plausible answers. That is, we propose an empirical solution to the who-problem and to the persistence-problem (...) on the basis of the new perspectives opened by a molecular understanding of epigenetic processes. In particular, concerning the former, we argue that any living being is the result of the epigenetic processes that have regulated the expression of its genome; concerning the latter, we defend the idea that the criterion for the persistence of its identity is to be indicated in the continuity of those epigenetic processes. We also counteract possible objections, in particular (1) whether our approach has something to say at a metaphysical level; (2) how it could account for the passage from the two phenotypes of the parental gametes to the single phenotype of the zygote; (3) how it could account for the identity of derivatives of one living being that continue to live disjoined from that original living being; (4) how it could account for higher mental functions. (shrink)