The Kramers-Kronig equations and the current methods used to apply them to electrochemical impedance spectra are reviewed. Measurement models are introduced as a tool for identification of the frequency-dependent error structure of impedance data and for evaluating the consistency of the data with the Kramers-Kronig relations. Through the use of a measurement model, experimental data can be checked for consistency with the Kramers-Kronig relations without explicit integration of the Kramers-Kronig relations; therefore, inaccuracies associated with extrapolation of an incomplete frequency spectrum are resolved. The measurement model can be used to determine whether the residual errors in the regression are due to an inadequate model, to failure of data to conform to the Kramers-Kronig assumptions, or to noise.