Somatic cell nuclear transfer (SCNT) is a technology by which a highly differentiated somatic nucleus is transferred into an enucleated oocyte to generate a reconstructed embryo that subsequently develops to an offspring. However, to date, the efficiency of cloned animal is still low. The major reason is incomplete nuclear reprogramming of donor cells after nuclear transfer, which results in abnormal epigenetic modifications, including DNA methylation, histone acetylation, gene imprinting, X-chromosome inactivation, and telomere length. Most improvements have been made in somatic epigenetic reprogramming with small molecules and manipulating expression of specific genes. It is expected that SCNT will soon have broad applications in both basic research and practical production. In this review, we summarize the recent progress in epigenetic reprogramming by somatic cell nuclear transfer; in particular, we focus on strategies for rescuing the epigenetic errors occurring during SCNT.