Aneuploidy is commonly seen in human preimplantation embryos, most particularly at the cleavage stage because of genome activation by third cell division. Aneuploid embryos have been used for the derivation of normal embryonic stem cell (ESC) lines and developmental modeling. This review addresses aneuploidies in human preimplantation embryos and human ESCs and the potential of self-correction of these aberrations. Diploid-aneuploid mosaicism is the most frequent abnormality observed; hence, embryos selected by preimplantation genetic diagnosis at the cleavage or blastocyst stage could be partly abnormal. Differentiation is known as the barrier for eliminating mosaic embryos by death and/or decreased division of abnormal cells. However, some mosaicisms, such as copy number variations could be compatible with live birth. Several reasons have been proposed for self-correction of aneuploidies during later stages of development, including primary misdiagnosis, allocation of the aneuploidy in the trophectoderm, cell growth advantage of diploid cells in mosaic embryos, lagging of aneuploid cell division, extrusion or duplication of an aneuploid chromosome, and the abundance of DNA repair gene products. Although more studies are needed to understand the mechanisms of self-correction as a rare phenomenon, most likely, it is related to overcoming mosaicism.