The mechanisms by which DNA polymerases achieve their remarkable fidelity, including base selection and proofreading, are briefly reviewed. Nine proofreading models from the current literature are evaluated in the light of steady-state and transient kinetic studies of E. coli DNA polymerase I, the best-studied DNA polymerase. One model is demonstrated to predict quantitatively the response of DNA polymerase I to three mutagenic probes of proofreading: exogenous pyrophosphate, deoxynucleoside monophosphates, and the next correct deoxynucleoside triphosphate substrate, as well as the response to combinations of these probes. The theoretical analysis allows elimination of many possible proofreading mechanisms based on the kinetic data. A structural hypothesis links the kinetic analysis with crystallographic, NMR and genetic studies. It would appear that DNA polymerase I proofreads each potential error twice, at the same time undergoing two conformational changes within a catalytic cycle. Multi-stage proofreading is more efficient, and may be utilized in other biological systems as well. In fact, recent evidence suggests that fidelity of transfer RNA charging may be ensured by a similar mechanism.