The present invention provides a genetic method of tethering polypeptides to the yeast cell wall in a form accessible for binding to macromolecules. Combining this method with fluorescence-activated cell sorting provides a means of selecting proteins with increased or decreased affinity for another molecule, altered specificity, or conditional binding. As one embodiment, attaching an scFv antibody fragment to the Aga2p agglutinin effectively mimics the cell surface display of antibodies by B cells in the immune system for affinity maturation in vivo. As another embodiment, T cell receptor mutants can be isolated by this method that are efficiently displayed on the yeast cell surface, providing a means of altering T cell receptor binding affinity and specificity by library screening.