Perovskite-type oxides are important in material sciences, physics and earth sciences. The ideal perovskite structure has an ABX 3 stoichiometry and belongs to the cubic space group Pm3m. However, there are several structural deviations from the ideal cubic structure, such as tetragonal I4/mcm, orthorhombic Pbnm and so on. Geometrically, the distorted structures could be described with several models, for example, the tolerance factor, octahedral tilting and global parameterization method (GPM). This paper reviews the geometric parameters of these models and discusses the relationship between the ideal and distorted structures. The structure of perovskite YbNiO 3 and the structural deviations of MgSiO 3 and ScAlO 3 under increasing hydrostatic pressures are theoretically predicted and compared with the available experimental data.