The prospect of transplanting cells and tissues without the risk of immune rejection or the need for powerful immunosuppressive drugs is the 'holy grail' of transplantation medicine. Now, with the advent of pluripotent stem cells, CRISPR-Cas9 and other gene-editing technologies, the race to create 'off-the-shelf' donor cells that are invisible to the immune system ('universal cells') has started. One important approach for creating such cells involves the manipulation of genes required for immune recognition, in particular HLA class I and II proteins. Other approaches leverage knowledge of immune-cloaking strategies used by certain bacteria, viruses, parasites, the fetus and cancer cells to induce tolerance to allogeneic cell-based therapies by modifying cells to express immune-suppressive molecules such as PD-L1 and CTLA4-Ig. Various academic groups as well as biotechnology and pharmaceutical companies are on the verge of bringing these therapies into the clinic.