MHC-encoded molecules govern adaptive immune responses by presenting peptides to T cell receptors (TCRs). Based on TCR-MHC crystal structures, we revisit the extent of TCR binding degeneracy, a property with important biological consequences because the diversity of TCR ligands that can be encountered exceeds the number of T cell clones present in a person at any one time. We also discuss whether the approximate diagonal binding of TCR on MHC molecules is due to an intrinsic property of the TCR variable regions, or results from the action of the CD4 and CD8 coreceptors during intrathymic T cell selection. Finally, we discuss how MHC restriction of antigen recognition might have emerged during evolution.