Vitrification is the process by which a liquid solidifies at temperatures usually far below the normal freezing point, but without the formation of any crystalline phase. The liquid has formed a glass. Occasionally, when the liquid consists of a solution, one of the components freezes to form a crystalline phase during cooling, but the remainder of the solution vitrifies. The product is then a partially crystallized glass. Glass formation, as a feature of aqueous solutions, either of the whole solution or of the remaining fraction after crystallization of ice, is discussed. We focus on the general principles involved in glass formation and also discuss in detail the effect of pressure on the nucleation and vitrification of the solution. In particular we look at the physical processes involved as well as the chemical aspects of the solutes which can be used in vitrifiable aqueous solutions. In any application of vitrification of aqueous solutions the material properties of the resultant glass are also important; these are also briefly considered. Recent work concerning the nature of the devitrification (crystallization during warming) event at high pressures is detailed.