Pressure is one of the essential thermodynamic variables that, due to some former experimental difficulties, was long known as the "forgotten variable." But this has changed over the last decade. This book includes the most essential first experiments from the 1960's and reviews the progress made in understanding glass formation with the application of pressure in the last ten years. The systems include amorphous polymers and glass-forming liquids, polypeptides and polymer blends. The thermodynamics of these systems, the relation of the structural relaxation to the chemical specificity, and their present and future potential applications are discussed in detail. The book provides (a) an overview of systems exhibiting glassy behavior in relation to their molecular structure and provides readers with the current state of knowledge on the liquid-to-glass transformation, (b) emphasizes the relation between thermodynamic state and dynamic response and (c) shows that the information on the pressure effects on dynamics can be employed in the design of materials for particular applications. It is meant to serve as an advanced introductory book for scientists and graduate students working or planning to work with dynamics. Several scientific papers dealing with the effects of pressure on dynamics have appeared in leading journals in the fields of physics in the last ten years. The book provides researchers and students new to the field with an overview of the knowledge that has been gained in a coherent and comprehensive way.