The structural chemistry of B2O3 has been the subject of considerable controversy in the literature, especially in the case of the vitreous phase. A brief review is presented as to the present state of knowledge concerning the structures of crystalline, liquid and vitreous B2O3, and it is demonstrated that the key to the structural chemistry of B2O3 lies in understanding that of the liquid state, which is dominated by the equilibrium reaction between B3O3 phi(3) boroxol groups and independent B phi(3) basic structural units (i.e. those not in boroxol groups): B3O3 phi(3) B-3 phi(3). The failure of the low pressure polymorph, B2O3-I, to form, either by crystallisation from the supercooled liquid at ambient pressure, or on devitrification of vitreous B2O3, is due to the high activation energy involved both in the break-up of boroxol groups and as a result of the large difference in number density between the crystal and supercooled liquid/glass. SAXS studies of vitreous and supercooled liquid B2O3 by V. V. Golubkov indicate that, in addition to the scattering due to thermal density fluctuations, there is extra small-Q scattering, centred at Q=0, arising from regions of inhomogeneity similar to 15 angstrom in size. These disappear for B2O3 equilibriated at temperatures below 240 degrees C, and are interpreted as being linked with the above equilibrium reaction. The fact that the time scale for establishing the equilibrium boroxol fraction, x(B), in the supercooled liquid state is very much longer than that associated with the thermal density fluctuations means that the structural rearrangements during quenching to the vitreous state are more complex than for SiO2, thus explaining the wide range of glass transition temperatures, T-g, and number densities, rho degrees, reported in the literature for vitreous B2O3. Golubkov's SAXS data also mitigate against a two-phase nanoheterogeneous structure for vitreous B2O3, based on nanodomains rich in either boroxol groups or independent B phi(3) triangles. Contrary to conventional wisdom, it is indeed possible to crystallise B2O3 from the supercooled liquid just above Tg. However, this takes considerable time, and the resulting long forgotten polymorph is not B2O3-I, but one that has an average number density within the range of that exhibited by the glass, and which almost certainly has a structure that includes boroxol groups.