Theoretical and experimental studies characterizing the status of the science of thermophoresis in gases at small Knudsen numbers (relative to the dimensions of the object) are analyzed. The known modifications of the theory of thermophoresis amount to an approximation linear in the Knudsen number, while the zero-order approximation corresponds to the result of Epstein. Analysis of the experimental data on thermophoresis of aerosols of high heat conductivity shows that, among all the experiments described in the literature, not one satisfies the requirements that allow one to perform a correct comparison with the theory. Also the results of experiments with aerosols (objects) of low heat conductivity are unsatisfactory. An original method of studying thermophoresis in gases is proposed.