Moment technique has been extensively used for the evaluation of the rate and equilibrium parameters in chemical reactors and also in adsorption vessels, for about five decades. Adsorption and reaction rate parameters, as well as axial dispersion constants, effective diffusivities within porous catalysts and heat and mass transfer coefficients were shown to be effectively evaluated by analyzing the moments of the response peaks, which could be obtained from pulse-response experiments performed in a reaction/adsorption vessel. A detailed review of chromatographic processes, involving moment analysis of adsorption equilibrium and rate constants in fixed beds, dynamic analysis of batch adsorbers, moment analysis of fluidized bed, slurry and trickle bed reactors are reported in this manuscript. Applications of the single-pellet moment technique, which was developed for the effective investigation of intrapellet rate and equilibrium processes, by eliminating the contributions of axial dispersion and external transport parameters, are comprehensively discussed. Recent studies for the analysis of reaction rate parameters using the TAP reactor approach, use of single pellet system for the investigation of catalytic and non-catalytic solid-gas reactions and extension of the moment technique to non-linear systems opened new pathways in reaction engineering research.