Transition-metal oxides (TMO) with the perovskite structure have a long history of research and have been known as materials with a variety of interesting properties, such as dielectric, magnetic, optical and transport properties. It was about a decade ago that the high-temperature superconducting (high Tc) cuprates with layered perovskite structures were discovered [1]. This was the first renewal of interest in the perovskite TMO which has produced advances in the control of the related materials and contributed to deeper understanding of their basic properties. The second renewal was brought in by the important recent activities on mainly perovskite manganites. Colossal magnetoresistance (CMR) [2-6], magnetic-field (H ) induced structural phase transitions [7] and unique phase diagrams in the T — H plane [8] are some examples of recent dramatic discoveries. It is true that many of the basic ingredients responsible to these phenomena were proposed fairly long time ago. They are, for example, double exchange [9-11], Jahn-Teller (JT) effect [12-14], charge ordering [15,16] and orbital ordering [17-19]. Nevertheless, it is still difficult to identify the real controlling mechanism of each phenomenon, because some different mechanisms can lead to very similar phenomena. For example, the electron-electron interaction and the JT effect can both induce the orbital ordering. Millis et al. [20] argued that not only the double exchange but also the dynamical JT effect will contribute to CMR. The importance of antiferromagnetic fluctuation in CMR was also pointed out [21].