Abstract: The concept of liquid fragility, firstly introduced byAngell in the 1980s, has provided new insight on thenature of glassy state and built a bridge between the glass-formed liquidsand the resulting solids. The study on the glass transition based on fragilityand Mode coupling theory or potential energy landscape has become an areaof intensive research in recent years. Exploring the correlationbetween the fragility of liquids and the basic property of the correspondingglass phase should be a promising field for mechanics. In this paper,the basic phenomena and several dominant theories about the glasstransition, the development of the relationship between the fragility andthe basic property of glasses are first reviewed, and then several pointsthat deserve further investigations in this field are proposed.