In his Science article of 1995, P.W. Anderson mentioned that “the deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition. This could be the next breakthrough in the coming decade.” Today (some 15 years later), we claim that he was right in this prediction. Especially over the last 10–15 years, there has been more progress in our understanding of glass formation than in the previous 40 years.
A unique feature of the molecular dynamics in glass-forming systems is the continuous and dramatic increase in the structural relaxation time, from values on the order of picoseconds up to hundreds of seconds in the vicinity of the glass “transition” temperature. Other transport quantities such as the diffusion constant or viscosity show a similar increase. Another important characteristic is the non-exponential character of the relaxation function. Although cooling a liquid is the method most often employed to induce the liquid-to-glass “transition,” this is not the only root towards the glassy state. Among others, a liquid can be vitrified by increasing pressure under isothermal conditions. This path was first exploited in the 1960s, but due to serious experimental difficulties in performing spectroscopic measurements under elevated pressures, it soon came to a standstill (and hence pressure became the “forgotten” thermodynamic variable). Nevertheless, such experiments are necessary to provide the complete physical description of the vitrification process. In recent years, we have witnessed a major breakthrough in the study of the dynamics of supercooled liquids and of the glass “transition” under elevated pressures, mainly by using dielectric spectroscopy and other methods (photon correlation spectroscopy, rheology, and NMR).