Alpha functions usually aim at predicting the thermodynamic properties of specific compounds in a limited range of reduced temperatures. The differences between polynomial alpha functions are mainly the functional forms and the parameter correlations. In this work, the functional forms, the parameter correlations, and the scope of 64 polynomial alpha functions are reviewed. The inherent relationships between the polynomial alpha functions as well as developing trends are also discussed. These functions were modified by changing the coefficients, exponents, or variable terms. The parameter formulas were re-correlated with the acentric factors or the other natural parameters. In recent years, research into polynomial alpha functions has mainly focused on reservoir fluids, and the alpha functions have been modified by adding characteristic constants of pseudo components to the equations or the parameter correlations. The Soave-type function has significant research value and will influence the development of polynomial alpha functions in the coming years.