Human pluripotent stem cells, which include embryonic stem cells and induced pluripotent cells (iPSCs), are capable of unlimited division and differentiation into all cells of the body. These cells are considered as a potential source of various types of cells for transplantations. The use of autologous iPSCs is not potentially associated with immune rejection and does not require immunosuppression required for allogeneic grafts. However, the high cost of this technology and the duration of obtaining iPSCs and differentiated cells may limit the use of autologous iPSCs in clinical practice. In addition, full equivalence and immunological compatibility of autologous iPSCs and their derivatives have been repeatedly questioned. One approach to solving the problem of the immunological compatibility of allogeneic derivatives of iPSCs can be the establishment of cell lines with reduced immunogenicity. Differentiated derivatives of such iPSCs may be suitable for transplantation to any patient. This review discusses the strategies for evading immune surveillance in normal and tumor processes that can be used to establish stem cell lines with reduced immunogenicity.