Mesenchymal stem cells (MSCs) are an adult stromal cell population possessing potent differentiation capacity and a potential for use across major histocompatibility complex barriers. Although allogeneic MSCs have potent immunosuppressive properties, evidence also suggests that they elicit a weak allogeneic immune response. However, the effect of induced differentiation on the immunosuppressive ability and immunogenicity of allogeneic MSCs is a potential obstacle when applying MSCs in tissue replacement therapies. These concerns will be explored in this review, with particular emphasis on changes in the cell surface expression of immunogenic markers, changes in the secretion of immunosuppressive molecules and in vivo functional benefits of the cell therapy. We review the literature from a translational point of view, focusing on pre-clinical studies that have utilised and analysed the effects of allogeneic immune responses on the ability of allogeneic MSCs to regenerate damaged tissue in models of bone, heart and cartilage defects.