We have known since the late 1980s that the function of classical major histocompatibility complex (MHC) class I molecules is to bind peptides and display them at the cell surface to cytotoxic T cells. Recognition by these sentinels of the immune system can lead to the destruction of the presenting cell, thus protecting the host from pathogens and cancer. Classical MHC class I molecules (MHC I hereafter) are co-dominantly expressed, polygenic, and exceptionally polymorphic and have significant sequence diversity. Thus, in most species, there are many different MHC I allotypes expressed, each with different peptide-binding specificity, which can have a dramatic effect on disease outcome. Although MHC allotypes vary in their primary sequence, they share common tertiary and quaternary structures. Here, we review the evidence that, despite this commonality, polymorphic amino acid differences between allotypes alter the ability of MHC I molecules to change shape (that is, their conformational plasticity). We discuss how the peptide loading co-factor tapasin might modify this plasticity to augment peptide loading. Lastly, we consider recent findings concerning the functions of the non-classical MHC I molecule HLA-E as well as the tapasin-related protein TAPBPR (transporter associated with antigen presentation binding protein-related), which has been shown to act as a second quality-control stage in MHC I antigen presentation.