The pressure effects on three different AlOOH structures (alpha, gamma, and beta phases) are systematically analyzed by density functional theory with different exchange and correlation energy functional approximations, namely two local, two generalized-gradient approximation (GGA), and two GGA for solids (GGAsol). Phase stability, compressibility and hydrogen bond evolution are studied in a range of pressures from 0 to 30 GPa. In general, the use of GGAsol functionals is mandatory in order to have the correct phase stability order, a good description of the hydrogen bonds, and a close agreement with the experimental lattice parameters at the various pressures. Pressure-induced hydrogen-bond symmetrization is found in gamma and beta phases at high compression, while the hydrogen bonds in the alpha phase remain asymmetric. A detailed analysis of the uncertainties on the values of the bulk moduli and their pressure derivative at zero pressure deduced by fitting calculated or experimental (P, V) data is also presented.