The history of electrochemical impedance spectroscopy (EIS) is briefly reviewed, starting with the foundations laid by Heaviside in the late 19th century in the form of Linear Systems Theory (LST). Warburg apparently was the first to extend the concept of impedance to electrochemical systems at the turn of the 19th century, when he derived the impedance function for a diffusional process that still bears his name. Impedance spectroscopy was next employed extensively using reactive bridges to measure the capacitance of ideally polarizable electrodes (mostly mercury), leading to the development of models for the electrified interface. However, it was the invention of the potentiostat in the 1940s and the development of frequency response analyzers in the 1970s that led to the use of EIS in exploring electrochemical and corrosion mechanisms, primarily because of their ability to probe electrochemical systems at very low frequencies. These inventions have led to an explosion in the use of EIS for exploring a wide range of systems and processes, ranging from conduction in the solid and liquid states, ionic and electronic conduction in polymers, heterogeneous reaction mechanisms, and the important phenomenon of passivity. It is evident that the use of EIS in identifying reaction mechanisms makes use of pattern recognition, currently through inspection. It is argued that, in the future development of EIS, reaction mechanism analysis (RMA) would be most efficiently done by using artificial neural networks operating in the pattern recognition mode. This strategy would require the creation of libraries of reaction mechanisms for which the theoretical impedance functions are known.