Abstract: With the development of hypersonic flight technology in the near space, accurate prediction of the transition location of hypersonic boundary layers is highly desired. Due to the difficulty of implementing hypersonic experiments, there is no enough experimental data to realize a semi-empirical method of transition prediction for high-speed flight vehicles as reliably as their low-speed counterparts. For that purpose, the physical process of transition needs to be understood more thoroughly, and based on which, a reasonable transition prediction method can be established. So far, for hypersonic boundary layers, the main uncertainties of transition prediction come from the first stage and the last stage of the transition respectively, i.e. the receptivity and the criterion of transition. This paper presents the recent progress and the problems remained in these two aspects, including the specific path in receptivity of a blunt cone boundary layer and the physical mechanism involved in transition induced by cross flow. For the stage of evolutions of disturbances, the integral strategy in applying e^N method to the three-dimensional boundary layer, and the intermodal exchange between the first mode and second mode encountered in hypersonic boundary layers are discussed. In conclusion, the problems and challenges are summarized for the improvement of transition prediction method based on linear stability theory.