A comparative study of theoretical models of different three-dimensional photonic bandgap (3D-PBG) structures has been performed, taking into account instability and convergence problems. Some rules for solving these problems and for reducing the computational time by finding symmetries in the structures are also explained. Finally, some applications produced by defects in 3D structures are shown by studying the creation of a complete bandgap in one of them and the variation of partial bandgaps in several 3D-PBG structures when several parameters of the defects, such as the number of layers stacked at each side of the defect, its thickness, and the real and imaginary parts of its index of refraction, are changed.