Cloning of bovine, pig and monkey etc. has been successful by nuclear transfer since “dolly” was born, but the overall efficiency of cloning is very low(typically between 0% and 3%), and many cloned animals display abnormalities in some degrees. Recent studies showed that the reprogramming of the genome that occurs during normal development is aberrant in cloned embryos, especially demethylation is inefficient. Progress in reprogramming of genome of early cloned embryos and the somatic nucleus remodeling in the recipient cytoplasm is reviewed in order to offer some clues to resolve the two important problems in cloning.