Clar's aromatic sextet theory provides a good means to describe the aromaticity of benzenoid hydrocarbons,
which was mainly based on experimental observations. Clar defined sextet pattern and Clar number of benzenoid hydrocarbons, and he observed that for isomeric benzenoid hydrocarbons, when Clar number increases the absorption
bands shift to shorter wavelength, and the stability of these isomers also increases. Motivated by Clar's aromatic sextet theory, three types of polynomials (sextet polynomial, Clar polynomial, and Clar covering polynomial) were defined, and
Randic´'s conjugated circuit model was also established. In this survey we attempt to review some advances on Clar's aromatic sextet theory and Randic´'s conjugated circuit model in the past two decades. New applications of these
polynomials to fullerenes, and calculation methods of linear independent and minimal conjugated circuit polynomials of benzenoid hydrocarbons are also presented.