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We report a joint experimental and theoretical investigation of the high-pressure structural and vibrational properties of terbium sesquioxide (Tb2O3). Powder x-ray diffraction and Raman scattering measurements show that cubic (C-type) Tb2O3 undergoes two phase transitions up to 25 GPa. We observe a first irreversible reconstructive transition to the monoclinic (B-type) phase at ~7 GPa and a subsequent reversible displacive transition from the monoclinic to the trigonal (A-type) phase at ~12 GPa. Thus, Tb2O3 is found to follow the well-known C-B-A phase transition found in other cubic rare-earth sesquioxides with cations of larger atomic mass than Tb. Our ab initio theoretical calculations predict phase transition pressures and bulk moduli for the three phases in rather good agreement with experimental results. Moreover, Raman-active modes of the three phases have been monitored as a function of pressure and lattice-dynamics calculations have allowed us to confirm the assignment of the experimental phonon modes in the C-type phase as well as to make a tentative assignment of the symmetry of most vibrational modes in the B- and A-type phases. Finally, we extract the bulk moduli and the Raman-active modes frequencies together with their pressure coefficients for the three phases of Tb2O3. These results are thoroughly compared and discussed in relation to those reported for rare-earth and other related sesquioxides. It is concluded that the evolution of the volume and bulk modulus of all the three phases of these technologically relevant compounds exhibit a nearly linear trend with respect to the third power of the ionic radii of the cations.