The liquid phase remains poorly understood. In many cases, the densities of liquids and their crystallized solid phases are similar, but since they are amorphous they lack the spatial order of the solid. Their dynamical properties change remarkably over a very small temperature range. At high temperatures, near their melting temperature, liquids flow easily under shear. However, only a few hundred degrees lower flow effectively ceases, as the liquid transforms into a solid-like glass. This temperature-dependent dynamical behavior is frequently characterized by the concept of kinetic fragility (or, generally, simply fragility). Fragility is believed to be an important quantity in glass formation, making it of significant practical interest. The microscopic origin of fragility remains unclear, however, making it also of fundamental interest. It is widely (although not uniformly) believed that the dynamical behavior is linked to the atomic structure of the liquid, yet experimental studies show that although the viscosity changes by orders of magnitude with temperature, the structural change is barely perceptible. In this article the concept of fragility is discussed, building to a discussion of recent results in metallic glass-forming liquids that demonstrate the presumed connection between structural and dynamical changes. In particular, it becomes possible to define a structural fragility parameter that can be linked with the kinetic fragility.