The concept of "fragility", which was introduced to characterize the degree of super-Arrhenius temperature dependence of the relaxation time and transport coefficients, has since been taken as a key quantity that seems to correlate with other properties of glass-forming liquids and polymers. With the goal of assessing the usefulness and the robustness of the concept, we address here several questions: How to best quantify fragility? How significant are the observed differences in fragility? Is fragility connected to "cooperativity" and collective behavior?