"Amorphous materials may be classified into three types – thermodynamically stable liquids, metastable (supercooled) liquids and solid glasses. The second type represents the meeting point of many of the great challenges of statistical physics and materials science. What is the mechanism of dynamical arrest, by which structural relaxation become progressively inhibited upon cooling from a liquid to a glass? Can we develop physical pictures of the sequence of fluctuations associated with irreversible relaxation in metastable liquids? How do crystals emerge from these fluctuations?Here we take a structural approach coupled with novel experiments and computer simulations to tackle two specific questions. Firstly, it has long been believed that there should be some structural mechanism underpinning the glass transition, where deeply supercooled liquids continuously transform into solid glasses. Secondly, the fate of the supercooled liquid – whether it crystallises on accessible timescales – should also be related to the local atomic arrangements in the liquid. Tackling the first will lead to insight into the nature of the glass transition - it is not known whether or not there is a true thermodynamic transition to a glass. As for crystallisation, predicted nucleation rates vary wildly with those obtained experimentally in the only system in which both have been compared, little is known beyond trial and error of means by which crystallisation in mixtures can be controlled. In short, our understanding of the fate of supercooled liquids is lacking in a variety of ways. Understanding the glass transition and nucleation is of fundamental importance, and both have important applications for example in metallic glasses and phase change materials. The former are prized for their superior mechanical properties such as extreme toughness while latter underpin emergent technologies such as optical data storage and phase change memory."