A Review of Liquid-Glass Transitions Anne C. Hanna ∗ December 14, 2006 Abstract Supercooling of almost any liquid can induce a transition to an amorphous solid phase. This does not appear to be a phase transition in the usual sense — it does not involved sharp discontinuities in any system parameters and does not occur at a well-defined temperature — instead, it is due to a rapid increase in the relaxation time of the material, which prevents it from reaching equilibrium on timescales accessible to experimentation. I will examine various models of this transition, including elastic, mode-coupling, and frustration-based explanations, and discuss some of the problems and apparent paradoxes found in these models. * University of Illinois at Urbana-Champaign, Department of Physics, email: ahanna@uiuc.edu