The pressure swing adsorption (PSA) models discussed here are divided into three categories: partial differential equation model, electrical analogue model and neural network model. The partial differential equation model, including equilibrium and kinetic models, has provided an elementary viewpoint for PSA processes. Using the simplest equilibrium models, some influential factors, such as pressurization with product, incomplete purge, beds with dead volume and heat effects, are discussed respectively. With several approximate assumptions i.e., concentration profile in adsorbent, "frozen" column, symmetry and heat effects of bed wall, the more complex kinetic models can be simplified to a certain degree at the expense of a limited application. It has also been found that the electrical analogue model has great flexibility to handle more realistic PSA processes without any additional hypothesis.