TCRs function by recognizing antigens that are processed and presented by MHC molecules. The MHC class I molecules present endogenous antigens to CD8+ T cells, while MHC class II molecules present exogenous antigens to CD4+ T cells. Upon antigen binding, the TCR undergoes a conformational change that triggers a signaling cascade through the CD3 complex, leading to T cell activation, proliferation, and differentiation.