Although epigenetic inheritance (EI) is a rapidly growing field of modern biology, it still has no clear place in fundamental genetic concepts which are traditionally based on the hereditary role of DNA. Moreover, not all mechanisms of EI attract the same attention, with most studies focused on DNA methylation, histone modification, RNA interference and amyloid prionization, but relatively few considering other mechanisms such as stable inhibition of plastid translation. Herein, we discuss all known and some hypothetical mechanisms that can underlie the stable inheritance of phenotypically distinct hereditary factors that lack differences in DNA sequence. These mechanisms include (i) regulation of transcription by DNA methylation, histone modifications, and transcription factors, (ii) RNA splicing, (iii) RNA-mediated post-transcriptional silencing, (iv) organellar translation, (v) protein processing by truncation, (vi) post-translational chemical modifications, (vii) protein folding, and (viii) homologous and non-homologous protein interactions. The breadth of this list suggests that any or almost any regulatory mechanism that participates in gene expression or gene-product functioning, under certain circumstances, may produce EI. Although the modes of EI are highly variable, in many epigenetic systems, stable allelic variants can be distinguished. Irrespective of their nature, all such alleles have an underlying similarity: each is a bimodular hereditary unit, whose features depend on (i) a certain epigenetic mark (epigenetic determinant) in the DNA sequence or its product, and (ii) the DNA sequence itself (DNA determinant; if this is absent, the epigenetic allele fails to perpetuate). Thus, stable allelic epigenetic inheritance (SAEI) does not contradict the hereditary role of DNA, but involves additional molecular mechanisms with no or almost no limitations to their variety.