p-V-T measurements have been carried out on a broad series of polymers and polymer blends. The effect of pressure on the glass transition temperature, T(g), and on related properties - increments of the coefficients of expansion, DELTAalpha, and compressibility, DELTAkappa, at T(g) - has been evaluated critically. The results are discussed in’ terms of the free volume, the order parameter, and the statistical mechanical theory. It is concluded that neither the simple ’free volume’ theory, nor the order parameter theory in the one order assumption predict correctly the observed behaviour. A possible explanation of the phenomena observed is offered assuming an expansion of the free volume, which is independent of the nature of the polymer. For the blends binary contacts between the components are discussed, with respect to interaction energy and to conformational rearrangements.