T cells recognise foreign antigen presented by antigen presenting cells at extremely low concentrations, and are able to discriminate between different ligands with high specificity. McKeithan's kinetic proofreading model is often invoked to explain this sensitivity and specificity of the T cell. In this paper, we analyse the strengths and limitations of this model, and suggest that it does not seem adequate to explain the observed degree of T cell sensitivity, specificity and robustness.