Recent findings on intriguing physical properties of new A-site-ordered perovskite structure oxides are reviewed. High-pressure and high-temperature conditions stabilize the square-coordinated Jahn-Teller Cu2+ ions in the original 12-fold-coordinated positions of the perovskite structure. The special-ordered arrangement of the square-coordinated A'O-4 units that align perpendicularly to each other sets a characteristic structural framework, and the presence of Cu2+ ions at the A' site and A'-B interactions play crucial roles for the diverse and intriguing physical properties.