Twenty-five years have passed since the birth of Dolly the sheep, the first mammalian clone produced by adult somatic cell nuclear transfer (SCNT). During that time, the main thrust of SCNT-related research has been the elucidation of SCNT-associated epigenetic abnormalities and their correction, with the aim of improving the efficiency of cloned animal production. Through these studies, it has become clear that some epigenomic information can be reprogrammed by the oocyte, while some cannot. Now we know that the imprinting memories in the donor genome, whether canonical (DNA-methylation-dependent) or noncanonical (H3K27me3-dependent), are not reprogrammed by SCNT. Thus, SCNT-derived embryos have the normal canonical imprinting and the erased noncanonical imprinting, both being inherited from the donor cells. The latter can cause abnormal phenotypes in SCNT-derived placentas arising from biallelic expressions of noncanonically imprinted genes. By contrast, repressive epigenomic information, such as DNA methylation and histone modifications, might be more variably reprogrammed, leaving room for technical improvements. Low-input analytical technologies now enable us to analyze the genome of gametes and embryos in a high-throughput, genome-wide manner. These technologies are being applied rapidly to the SCNT field, providing evidence for incomplete reprogramming of the donor genome in cloned embryos or offspring. Insights from the study of epigenetic phenomena in SCNT are highly relevant for our understanding of the mechanisms of genomic reprogramming that can induce totipotency in the mammalian genome.