We report an experimental and theoretical lattice dynamics study of antimony telluride (Sb2Te3) up to 26 GPa together with a theoretical study of its structural stability under pressure. Raman-active modes of the low-pressure rhombohedral (R-3m) phase were observed up to 7.7 GPa. Changes of the frequencies and linewidths were observed around 3.5 GPa where an electronic topological transition was previously found. Raman-mode changes evidence phase transitions at 7.7, 14.5, and 25 GPa. The frequencies and pressure coefficients of the new phases above 7.7 and 14.5 GPa agree with those calculated for the monoclinic C2/m and C2/c structures recently observed at high pressures in Bi2Te3 and also for the C2/m phase in the case of Bi2Se3 and Sb2Te3. Above 25 GPa no Raman-active modes are observed in Sb2Te3, similarly to the case of Bi2Te3 and Bi2Se3. Therefore, it is possible that the structure of Sb2Te3 above 25 GPa is the same disordered bcc phase already found in Bi2Te3 by x-ray diffraction studies. Upon pressure release, Sb2Te3 reverts back to the original rhombohedral phase after considerable hysteresis. Raman- and IR-mode symmetries, frequencies, and pressure coefficients in the different phases are reported and discussed.