"Liquid fragility" is a concept that has been widely used in the investigation on the glass community, though it was presented less than two decades ago. The concept enables the comparison between the glass-forming liquids with different dynamic characters by using a general criterion, in which the temperature scale is reduced by the glass transition temperature. In order to illuminate the significance of the concept in the fields of the glass transition, structural relaxation process and the structure of supercooled liquids, the accomplished progress and the faced challenges are summarized from different aspects such as on the correlation between dynamics and thermodynamic characters of condensed matters, on the energy landscape, on the nonexponential relaxation and on the theoretical model of microstructure and medium-range order. The tendency of investigation in "liquid fragility" is also evaluated.