Large GaN single-crystal substrates with low dislocation density are the key materials for the commercial production of GaN-based laser diodes. We developed a new method to reduce the dislocations, named dislocation elimination by the epitaxial-growth with inverse-pyramidal pits (DEEP). A thick GaN film is epitaxially grown on a GaAs substrate with hydride vapor-phase epitaxy and then is separated from the GaAs substrate. The thick GaN layer grows with numerous large inverse-pyramidal pits. As the growth proceeds, dislocations in the GaN film are concentrated to the center of the pit and a wide area with low dislocation density is formed within the pit except the center area. To control the dislocation artificially, the position of the pits is fixed at a predetermined position by means of the selective growth of different polarity GaN film. This process was named as advanced DEEP (A-DEEP).GaN substrates with the A-DEEP method satisfied all the requirements for the violet laser diodes. We continued to develop new GaN substrates such as large-diameter c-plane substrates as well as nonpolar/semipolar GaN substrates. In particular, we overcame the green gap problem and developed the world's first true green laser diodes by selecting an optimal crystal plane.