It is sometimes said that glass in very old churches is thicker at the bottom than at the top because glass is a liquid, and so over several centuries it has flowed towards the bottom.  This is not true.  In Mediaeval times panes of glass were often made by the Crown glass process.  A lump of molten glass was rolled, blown, expanded, flattened and finally spun into a disc before being cut into panes.  The sheets were thicker towards the edge of the disc and were usually installed with the heavier side at the bottom.  Other techniques of forming glass panes have been used but it is only the relatively recent float glass processes which have produced good quality flat sheets of glass.

To answer the question "Is glass liquid or solid?" we have to understand its thermodynamic and material properties.

There is still much about the molecular physics and thermodynamics of glass that is not well understood, but we can give a general account of what is thought to be the case.

Many solids have a crystalline structure on microscopic scales.  The molecules are arranged in a regular lattice.  As the solid is heated the molecules vibrate about their position in the lattice until, at the melting point, the crystal breaks down and the molecules start to flow.  There is a sharp distinction between the solid and the liquid state, that is separated by a first order phase transition, i.e. a discontinuous change in the properties of the material such as density.  Freezing is marked by a release of heat known as the heat of fusion.

A liquid has viscosity, a measure of its resistance to flow.  The viscosity of water at room temperature is about 0.01 poises.  A thick oil might have a viscosity of about 1.0 poise.  As a liquid is cooled its viscosity normally increases, but viscosity also has a tendency to prevent crystallisation.  Usually when a liquid is cooled to below its melting point, crystals form and it solidifies; but sometimes it can become supercooled and remain liquid below its melting point because there are no nucleation sites to initiate the crystallisation.  If the viscosity rises enough as it is cooled further, it may never crystallise.  The viscosity rises rapidly and continuously, forming a thick syrup and eventually an amorphous solid.  The molecules then have a disordered arrangement, but sufficient cohesion to maintain some rigidity.  In this state it is often called an amorphous solid or glass.

Some people claim that glass is actually a supercooled liquid because there is no first order phase transition as it cools.  In fact, there is a second order transition between the supercooled liquid state and the glass state, so a distinction can still be drawn.  The transition is not as dramatic as the phase change that takes you from liquid to crystalline solids.  There is no discontinuous change of density and no latent heat of fusion.  The transition can be detected as a marked change in the thermal expansivity and heat capacity of the material.

The temperature at which the glass transition takes place can vary according to how slowly the material cools.  If it cools slowly it has longer to relax, the transition occurs at a lower temperature and the glass formed is more dense.  If it cools very slowly it will crystallise, so there is a minimum limit to the glass transition temperature.

A liquid to crystal transition is a thermodynamic one; i.e. the crystal is energetically more favourable than the liquid when below the melting point.  The glass transition is purely kinetic: i.e. the disordered glassy state does not have enough kinetic energy to overcome the potential energy barriers required for movement of the molecules past one another.  The molecules of the glass take on a fixed but disordered arrangement.  Glasses and supercooled liquids are both metastable phases rather than true thermodynamic phases like crystalline solids.  In principle, a glass could undergo a spontaneous transition to a crystalline solid at any time.  Sometimes old glass devitrifies in this way if it has impurities.

The situation at the level of molecular physics can be summarised by saying that there are three main types of molecular arrangement:

[Just to illustrate that no such classification could ever be complete, recently scientists have succeeded in making quasi-crystals that are quasi-periodic.  They do not fit into the above scheme and are sometimes described as being halfway between crystals and glass.]

It would be convenient if we could conclude that glassy materials changed from being a supercooled liquid to an amorphous solid at the glass transition, but this is very difficult to justify.  Polymerised materials such as rubber show a clear glass transition at low temperatures but are normally considered to be solid in both the glass and rubber conditions.

It is sometimes said that glass is therefore neither a liquid nor a solid.  It has a distinctly different structure with properties of both liquids and solids.  Not everyone agrees with this terminology.