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To delve deeper into the kinetics involved in the staging phenomena of lithium insertion into graphite, it is necessary to develop theoretical models that emulate the physical phenomenon involved. In the present work kinetic Monte Carlo simulations are used to carry out a thorough analysis of the Li-ion graphite system, with the twofold aim of providing atomistic support for interpretations based on several experimental electrochemical techniques commonly used in the laboratory and of making theoretical predictions for future experimental work. Cyclic voltammograms and chronoamperometric transients are obtained, and diffusion coefficients and exchange current densities are calculated at different Li loadings of graphite. These results are compared with selected experimental data from the literature. In this way, there emerge details that cannot be observed in ordinary experiments due to methodological/instrumental limitations. For example, it is found that chronoamperometric responses are different for intercalation and deintercalation, the latter being a faster process. The reason why these phenomena are different is revealed, supporting and widening experimental assumptions. The present results also suggest that the intrinsic hysteresis observed in experimental work (and in simulations) is due to kinetic factors. • Kinetic Monte Carlo simulations emulate electrochemical techniques allowing a deep atomistic study. • Cyclic voltammetry and chronoamperometric simulations profiles provide understanding on experimental results. • Diffusion coefficients and exchange current density predict the behavior of Li-ion in different intercalation levels. • Deintercalation is faster than intercalation, due to the Li-ion clog next to the interphase in the lithiation. • The hysteresis phenomenon is apparently related to a kinetic origin. [ABSTRACT FROM AUTHOR]