Using ab initio simulations and high-pressure experiments in a diamond anvil cell, we show that alumina (Al(2)O(3)) adopts the CaIrO(3)-type structure above 130 GPa. This finding substantially changes the picture of high-pressure behavior of alumina; in particular, we find that perovskite structure is never stable for Al(2)O(3) at zero Kelvin. The CaIrO(3)-type phase suggests a reinterpretation of previous shock-wave experiments and has important implications for the use of alumina as a window material in shock-wave experiments. In particular, the conditions of the stability of this phase correspond to those at which shock-wave experiments indicated an increase of the electrical conductivity. If this increase is caused by high ionic mobility in the CaIrO(3)-type phase of Al(2)O(3), similar effect can be expected in the isostructural postperovskite phase of MgSiO(3) (which is the dominant mineral phase in the Earth's D'' layer). The effect of the incorporation of Al on the perovskite/postperovskite transition of MgSiO(3) is discussed.