Interpretation of impedance spectroscopy data requires both a description of the chemistry and physics that govern the system and an assessment of the error structure of the measurement. The approach presented here includes use of graphical methods to guide model development, use of a measurement model analysis to assess the presence of stochastic and bias errors, and a systematic development of interpretation models in terms of the proposed reaction mechanism and physical description. Application to corrosion, batteries, and biological systems is discussed, and emerging trends in interpretation and implementation of impedance spectroscopy are presented.