It is now approximately 25 years since the sheep Dolly, the first cloned mammal where the somatic cell nucleus from an adult donor was used for transfer, was born. So far, somatic cell nucleus transfer, where G1-phase nuclei are transferred into cytoplasts obtained by enucleation of mature metaphase II (MII) oocytes followed by the activation of the reconstructed cells, is the most efficient approach to reprogram/remodel the differentiated nucleus. In general, in an enucleated oocyte (cytoplast), the nuclear envelope (NE, membrane) of an injected somatic cell nucleus breaks down and chromosomes condense. This condensation phase is followed, after subsequent activation, by chromatin decondensation and formation of a pseudo-pronucleus (i) whose morphology should resemble the natural postfertilization pronuclei (PNs). Thus, the volume of the transferred nuclei increases considerably by incorporating the content released from the germinal vesicles (GVs). In parallel, the transferred nucleus genes must be reset and function similarly as the relevant genes in normal embryo reprogramming. This, among others, covers the relevant epigenetic modifications and the appropriate organization of chromatin in pseudo-pronuclei. While reprogramming in SCNT is often discussed, the remodeling of transferred nuclei is much less studied, particularly in the context of the developmental potential of SCNT embryos. It is now evident that correct reprogramming mirrors appropriate remodeling. At the same time, it is widely accepted that the process of rebuilding the nucleus following SCNT is instrumental to the overall success of this procedure. Thus, in our contribution, we will mostly focus on the remodeling of transferred nuclei. In particular, we discuss the oocyte organelles that are essential for the development of SCNT embryos.