Recent computational modeling studies of configurational degrees of freedom in oxide-hydroxides of aluminum and copper are reviewed. Density functional theory calculations are employed to investigate the effect of hydrogen on the structural stability of gamma-alumina and to explore the configurational space of cuprous hydroxide CuOH. Free energy modeling, taking into account configurational and vibrational degrees of freedom, shows that the studied hydrogenated oxides of aluminum and copper are metastable compounds, whereas the respective oxides are thermodynamically stable phases. Selected structural and optical properties of the studied compounds, evaluated using a hybrid functional approach, are reported and compared with available experimental data.