The potential to develop into any cell type makes human pluripotent stem cells (hPSCs) one of the most promising sources for regenerative treatments. Hurdles to their clinical applications include (1) formation of heterogeneously differentiated cultures, (2) the risk of teratoma formation from residual undifferentiated cells, and (3) immune rejection of engrafted cells. The recent production of human isogenic (genetically identical) induced PSCs (hiPSCs) has been proposed as a "solution" to the histocompatibility barrier. In theory, differentiated cells derived from patient-specific hiPSC lines should be histocompatible to their donor/recipient. However, propagation, maintenance, and non-physiologic differentiation of hPSCs in vitro may produce other, likely less powerful, immune responses. In light of recent progress towards the clinical application of hPSCs, this review focuses on two antigen presentation phenomena that may lead to rejection of isogenic hPSC derivates: namely, the expression of aberrant antigens as a result of long-term in vitro maintenance conditions or incomplete somatic cell reprogramming, and the unbalanced presentation of receptors and ligands involved in immune recognition due to accelerated differentiation. Finally, we discuss immunosuppressive approaches that could potentially address these immunological concerns.