Electrochemical insertion-deintercalation reactions are typically associated with significant change in molar volume of the host compound. This strong coupling between ionic currents and strains underpins image formation mechanisms in electrochemical strain microscopy (ESM), and allows exploring the tip-induced electrochemical processes locally. Here we analyze the signal formation mechanism in ESM, and develop the analytical description of operation in frequency and time domains. The ESM spectroscopic modes are compared to classical electrochemical methods including potentiostatic and galvanostatic intermittent titration, and electrochemical impedance spectroscopy. This analysis illustrates the feasibility of spatially resolved studies of Li-ion dynamics on the sub-10-nm level using electromechanical detection.