As Christian Binek said this is the point of a large debate. I belong to the large community of people which does not believe that glass transition is a genuine phase transition. Hystorically, the hypothesis of a glass transition must be ascribed to W. Kauzmann which detected that at enough low temperatures the (configurational) entropy of an undercooled liquid should become lower than that of the corresponding solid phase at the same temperature. The extrapolation of this results towards absolute zero leads to the apparent violation of the 3rd law of thermodynamics. A possible way to avoid such a themodynamic crisis consisted in postulatic a second order phase transition at a temperature higher than the Kauzmann temperature. The mistake in the Kauzamann argument can be immediately individuated in the occurrence that he compared the entropy of the two states (the metastable liquid state and the stable solid one) but he completely disregarded their enthalpies. In few words, he explicitely assumed the possibility of an isothermal process which can drive the system from the metastable equilibrium to the stable one. This is clearly an erroneous assumption since the process we are dealing with is definitely an irreversible process. When crossing the boundary between the metastable and the stable equilibrium basins, the system does it so quickly that there is no time for heat exchange between the system itself and any outer thermal reservoir. So the process is isoenthalpic and not isothermal. When a supercooled liquid escape from metastable equilibrium it reaches a stable equilibrium condition which consists in a mixture of liquid and solid at the coexistence temperature (definitely higher of the starting temperature). Such a result can be esily verified experimentally and it is well known to people involved in atmosphere physics or in metallurgy: it is known as recalescence. Unfortunately, the Kauzmann mistake still survives and many people working with numerical simulation still describes the system in contact with a ideal reservoir which ensures the isothermal process. But such an assumption implyes an infinite conductivity of the system, which is an unphysical condition. On this basis the original motivation which suggested the hypothesis of a glass transition disappears. For sure, a glass looks different from a liquid since their transport properties are clearly different. But the question is if really the system has lost some degrees of freedom or if more simply they appear not relaxing over any experimentally possible time of scale. If one would adopt such a simpler perspective one should conclude that the glass state is not a (metastable) equilibrium condition but just refer to an out of equilibrium condition. So the so called glass transition would be not a thermodynamic transition but should be kinetic in character. This remains the very point of the debate.

And I have to admit that none of the proposed solution can represent a not ambiguous answer. The search for a sure answer face us with the trouble of describing highly irreversible processes, i. e. with non linear responce of the system to the thermodynamic fluctuation. Without any safe answer I prefer to adopt the simplest possible scenario. But this could be just question of opinions.

This is an ongoing debate, but my take and that of many others is it that the glass transition is an actual phase transition. One can define a glass order parameter. The situation is best studied in spin-glasses. People investigate, e.g., the non-linear susceptibility and use its divergence as criterion for criticality. Now this is where the discussion starts. Entire libraries can be filled with the research in this field. I am sure you will get plenty of answers.

As Christian Binek said this is the point of a large debate. I belong to the large community of people which does not believe that glass transition is a genuine phase transition. Hystorically, the hypothesis of a glass transition must be ascribed to W. Kauzmann which detected that at enough low temperatures the (configurational) entropy of an undercooled liquid should become lower than that of the corresponding solid phase at the same temperature. The extrapolation of this results towards absolute zero leads to the apparent violation of the 3rd law of thermodynamics. A possible way to avoid such a themodynamic crisis consisted in postulatic a second order phase transition at a temperature higher than the Kauzmann temperature. The mistake in the Kauzamann argument can be immediately individuated in the occurrence that he compared the entropy of the two states (the metastable liquid state and the stable solid one) but he completely disregarded their enthalpies. In few words, he explicitely assumed the possibility of an isothermal process which can drive the system from the metastable equilibrium to the stable one. This is clearly an erroneous assumption since the process we are dealing with is definitely an irreversible process. When crossing the boundary between the metastable and the stable equilibrium basins, the system does it so quickly that there is no time for heat exchange between the system itself and any outer thermal reservoir. So the process is isoenthalpic and not isothermal. When a supercooled liquid escape from metastable equilibrium it reaches a stable equilibrium condition which consists in a mixture of liquid and solid at the coexistence temperature (definitely higher of the starting temperature). Such a result can be esily verified experimentally and it is well known to people involved in atmosphere physics or in metallurgy: it is known as recalescence. Unfortunately, the Kauzmann mistake still survives and many people working with numerical simulation still describes the system in contact with a ideal reservoir which ensures the isothermal process. But such an assumption implyes an infinite conductivity of the system, which is an unphysical condition. On this basis the original motivation which suggested the hypothesis of a glass transition disappears. For sure, a glass looks different from a liquid since their transport properties are clearly different. But the question is if really the system has lost some degrees of freedom or if more simply they appear not relaxing over any experimentally possible time of scale. If one would adopt such a simpler perspective one should conclude that the glass state is not a (metastable) equilibrium condition but just refer to an out of equilibrium condition. So the so called glass transition would be not a thermodynamic transition but should be kinetic in character. This remains the very point of the debate.

And I have to admit that none of the proposed solution can represent a not ambiguous answer. The search for a sure answer face us with the trouble of describing highly irreversible processes, i. e. with non linear responce of the system to the thermodynamic fluctuation. Without any safe answer I prefer to adopt the simplest possible scenario. But this could be just question of opinions.

This is why it is a debate I guess. One major problem is that the dynamics becomes so slow on approaching the glass temperature (let me not call it glass transition out of respect for the above point of view). That makes it experimentally more than challenging to come to a conclusion. As an experimentalist one can have a look at theoretical predictions how this slowing down is supposed to happen and measure e.g. the frequency dependence of the susceptibility. Again the group of phase transition enthusiasts will find their predictions confirmed via the concept of a dynamical critical exponent. A wonderful anecdote is about an experiment taking place in the time domain. It is the pitch-drop experiment running now for 85 years http://en.wikipedia.org/wiki/Pitch_drop_experiment .

Http://phys.org/news/2013-07-scientists-reveal-supercooled-liquid.html#nwlt

Scientists reveal structure of a supercooled liquid