Strongly correlated electronic systems with ABO3 perovskite and/or perovskite-like structures have received much attention. High pressure is an effective method to prepare perovskites, in particular A-site and/or B-site ordered perovskites. In these ordered perovskites, both A and B sites can accommodate transition-metal ions, giving rising to multiple magnetic and electrical interactions between A-A, B-B, and A-B sites. The presence of these new interactions can induce a wide variety of interesting physical properties. In this review paper, we will introduce an A-site ordered perovskite with chemical formula AA3'B4O12 and two A- and B-site ordered perovskites with chemical formula AA3'B2B2'O12. All of these compounds can be synthesized only under high pressure. In the A-site ordered LaMn3Cr4O12 with cubic perovskite structure, magnetoelectric multiferroicity with new multiferroic mechanism is found to occur. This is the first observation of multiferroicity appearing in cubic perovskite, thereby opening the way to exploring new multiferroic materials and mechanisms. In the A- and B-site ordered perovskite CaCu3Fe2Os2O12, a high ferrimagnetic Curie temperature is observed to be around 580 K. Moreover, this compound exhibits semiconducting conductivity with an energy band gap of about 1 eV. The CaCu3Fe2Os2O12 thus provides a rare single-phase ferrimagnetic semiconductor with high spin ordering temperature well above room temperature as well as considerable energy band gap. Moreover, theoretical calculations point out that the introducing of A'-site Cu2+ magnetic ions can generate strong Cu-Fe and Cu-Os spin interactions. As a result, this A- and B-site ordered perovskite has a much higher Curie temperature than that of the B-site only ordered perovskite Ca2FeOsO6 (~320 K). In addition, we also for the first time prepare another A- and B-site ordered perovskite LaMn3Ni2Mn2O12. In the reported ordered perovskites with Mn3+ at the A' site, the A'-B intersite spin interaction is usually negligible. In our LaMn3Ni2Mn2O12, however, there exists the considerable A'-B interaction, which is responsible for the rare formation of B-site orthogonal spin structure with net ferromagnetic moment.