A very unusual ordered arrangement of the A-site ions produces AA'3B4O12 complex perovskites. The A site accommodates alkaline metals, alkaline-earth metals, and lanthanides like those in simple perovskites. At the originally 12-fold coordinated A' site, transition-metal ions such as Cu2+ and Mn3+ form square coordinated units that align perpendicular to each other. The presence of the transition-metal ions at the A' site produces A'-A' and and/or A'-B interactions in addition to B-B interaction usually seen in simple perovskite materials. Competitive and/or cooperative interplay of these interactions gives rise to diverse and intriguing physical properties. Two new A-site ordered perovskite structure oxides, CaCu3Fe4O12 and LaCu3Fe4O12, are highlighted.They were synthesized under high-pressure and high-temperature conditions. The compounds contain unusually high valence states of iron: Fe4+ in CaCu3Fe4O12 and Fe3.75+ in LaCu3Fe4O12. Instabilities of the high oxidation states at low temperatures are resolved in CaCu3Fe4O12 by charge disproportionation from Fe4+ to Fe3+ and Fe5+ and in LaCu3Fe4O12 by charge transfer between A-site Cu and B-site Fe ions. The charge disproportionation and the charge transfer are accompanied by significant changes in structural, transport, and magnetic properties.