Glasses can be formed by many routes. In some cases, distinct polyamorphic forms are found. The normal mode of glass formation is cooling of a viscous liquid. Liquid behavior during cooling is classified between "strong" and "fragile," and the three canonical characteristics of relaxing liquids are correlated through the fragility. Strong liquids become fragile liquids on compression. In some cases, such conversions occur during cooling by a weak first-order transition. This behavior can be related to the polymorphism in a glass state through a recent simple modification of the van der Waals model for tetrahedrally bonded liquids. The sudden loss of some liquid degrees of freedom through such first-order transitions is suggestive of the polyamorphic transition between native and denatured hydrated proteins, which can be interpreted as single-chain glass-forming polymers plasticized by water and cross-linked by hydrogen bonds. The onset of a sharp change in d<r^2>/dT(<r^2> is the Debye-Waller factor and T is temperature) in proteins, which is controversially indentified with the glass transition in liquids, is shown to be general for glass formers and observable in computer simulations of strong and fragile ionic liquids, where it proves to be close to the experimental glass transition temperature. The latter may originate in strong anharmonicity in modes ("bosons"), which permits the system to access multiple minima of its configuration space. These modes, the Kauzmann temperature T_K, and the fragility of the liquid, may thus be connected.