We consider the behaviour of nanophase materials under high pressure thermodynamic conditions along the room temperature isotherm. Concurrent high temperatures exceeding a few hundred degrees at high pressure are avoided to ensure that no grain-coarsening occurs, in which case there may be a reversion back to investigating bulk behavior. The effect of pressure in the bulk is normally to induce a structural transition to a high pressure phase which has the lowest Gibbs free energy in P-T phase space. What are the implications for such phase transitions in ultrafine nanophase materials with grain sizes approaching critical dimensions, d∼10 nm in some systems? More than one quarter of the total atoms in such a nano-grain are constituted in the surface, and the surface energy cost involved in the formation of a new phase is significant. The pressure response of ultrafine nano-materials will be exemplified by the anatase polymorph of TiO2 a highly topical wide band-gapmaterial. Anatase is particularly useful in this respect because the pressure response is not sensitively dependent on the quality (e.g., stoichiometry) of the sample, nor on whether a pressure transmitting medium for quasi-hydrostaticity is used or not. The implications of nanometer size grains on the known pressure-induced phase transitions of anatase have been investigated up to 30-40 GPa, using synchrotron XRD complemented by laser Raman measurements. At room temperature the bulk material undergoes a crystallographic transition from the tetragonal structure to the orthorhombic _-PbO2-type structure at 2-5 GPa, and then to the monoclinic baddeleyite phase at 12-15 GPa. The pressure response of ultrafine nano-anatase of d ( 10 nm grain size, is shown to be radically different to that of its macro-crystalline analog [1,2]. The anatase polymorph is stable to appreciably higher pressure than in bulk. In these ultrafine nano-anatase samples long range order eventually collapses at P > 20 GPa, although signatures of short-range ’’crystallinity’’ of the anatase polymorph are apparent up to the highest pressure of this study. The ’’ultra-stability’’ of nano-anatase is specific to grain sizes of d∼10 nm and below. This may be rationalised in terms of the thermodynamics involved in a mechanism of nucleation and growth of a new phase, and partly by usingMD simulations for the ultrafine samples where computational work is tractable. The effect of grain-size onmechanical properties (e.g., compressibility-ductility) is also deduced from the pressure response (P-V EOS data). The inverse Hall-Petch relationship explains the maximum or plateau in stiffness-hardness at a critical value of small grain size. There will be brief mention of the pressure response of other nanophase systems.