Since the discovery of human embryonic stem cells (hESC) and human-induced pluripotent stem cells (hiPSC), great hopes were held for their therapeutic application including disease modeling, drug discovery screenings, toxicological screenings and regenerative therapy. hESC and hiPSC have the advantage of indefinite self-renewal, thereby generating an inexhaustible pool of cells with, e.g., specific genotype for developing putative treatments; they can differentiate into derivatives of all three germ layers enabling autologous transplantation, and via donor-selection they can express various genotypes of interest for better disease modeling. Furthermore, drug screenings and toxicological screenings in hESC and hiPSC are more pertinent to identify drugs or chemical compounds that are harmful for human, than a mouse model could predict. Despite continuing research in the wide field of therapeutic applications, further understanding of the underlying basic mechanisms of stem cell function is necessary. Here, we summarize current knowledge concerning pluripotency, self-renewal, apoptosis, motility, epithelial-to-mesenchymal transition and differentiation of pluripotent stem cells.