Adsorption processes are widely used in different technological areas and industry sectors, thus continuously attracting attention in the scientific research and publications. Design and scale-up of these processes are essentially based on the knowledge and understanding of the adsorption kinetics and mechanism. Adsorption kinetics is usually modeled by using several well-known models including the pseudo-first and pseudo-second order models, the Elovich equation, and the intra-particle diffusion based models. However, in the scientific literature there are a significant number of cases with the inappropriate use of these models, utilization of erroneous expressions, and incorrect interpretation of the obtained results. This paper is especially focused on applications of the pseudo-second order, intra-particle diffusion and the Weber-Morris models, which are illustrated with typical examples. Finally, general recommendations for selection of the appropriate kinetic model and model assumptions, data regression analysis, and evaluation and presentation of the obtained results are outlined.