Human-induced pluripotent stem cells (hiPSCs) offer numerous possibilities in science and medicine, particularly when combined with precise genome editing methods. hiPSCs are artificially generated equivalents of human embryonic stem cells (hESCs), which possess an unlimited ability to self-renew and the potential to differentiate into any cell type of the human body. Importantly, generating patient-specific hiPSCs enables personalized drug testing or autologous cell therapy upon differentiation into a desired cell line. However, to ensure the highest standard of hiPSC-based biomedical products, their safety and reliability need to be proved. One of the key factors influencing human pluripotent stem cell (hPSC) characteristics and function is oxygen concentration in their microenvironment. In recent years, emerging data have pointed toward the beneficial effect of low oxygen pressure (hypoxia) on both hiPSCs and hESCs. In this review, we examine the state-of-the-art research on the oxygen impact on hiPSC functions and activity with an emphasis on their niche, metabolic state, reprogramming efficiency, and differentiation potential. We also discuss the similarities and differences between PSCs and cancer stem cells (CSCs) with respect to the role of oxygen in both cell types.