At the glass transition, no thermodynamic anomalies or diverging length scales in static properties have been
seen so far experimentally. On the other hand, dynamical correlation functions diverge at the transition and
show rich features over many orders of magnitude in time. One approach to explain glassy dynamics is the
framework of mode-coupling theory: The equations of motion for density correlation functions in a fluid are
approximated self-consistently and in the long-time limit yield glass-transition singularities. Such
singularities are known from caustics in optics (e.g. seen in rainbows and coffee mugs), and in fluids they
explain many features in glassy dynamics.
In addition to liquid-glass transitions, the theory predicts glass-glass transitions. These glass-glass
transitions are a consequence of the mathematical structure of the theory, and their experimental confirmation
therefore lends credibility to the theory. The mathematical features and dynamical predictions of the theory
shall be demonstrated with data from colloidal suspensions, liquid water, and static granular matter.