The structural properties of Thallium (III) oxide (Tl2O3) have been studied both experimentally and theoretically under compression at room temperature. X-ray powder diffraction measurements up to 37.7 GPa have been complemented with ab initio total-energy calculations. The equation of state of Tl2O3 has been determined and compared to related compounds. It has been found experimentally that Tl2O3 remains in its initial cubic bixbyite-type structure up to 22.0 GPa. At this pressure, the onset of amorphization is observed, being the sample fully amorphous at 25.2 GPa. The sample retains the amorphous state after pressure release. To understand the pressure-induced amorphization process, we have studied theoretically the possible high-pressure phases of Tl2O3. Although a phase transition is theoretically predicted at 5.8 GPa to the orthorhombic Rh2O3-II-type structure and at 24.2 GPa to the orthorhombic α-Gd2S3-type structure, neither of these phases were observed experimentally, probably due to the hindrance of the pressure-driven phase transitions at room temperature. The theoretical study of the elastic behavior of the cubic bixbyite-type structure at high-pressure shows that amorphization above 22 GPa at room temperature might be caused by the mechanical instability of the cubic bixbyite-type structure which is theoretically predicted above 23.5 GPa.