Novel functions and properties of transition-metal oxides such as high-temperature superconductivity and colossal magneto-resistance effect have attracted much attention. In these compounds, strong Coulomb interaction between electrons plays a significant role and it is believed that characterizations of local electronic states are important to make clear the mechanisms of the functions. We have performed scanning tunneling microscopy/spectroscopy to investigate local electronic states of two model compounds, Ca_2-xNa_xCuO₂Cl₂ and Sr₃Ru₂O₇, which are a high-temperature superconductor and an itinerant metamagnet, respectively. In Ca_2-xNa_xCuO₂Cl₂, we discovered a checkerboard-like modulation of the local density of states (LDOS) in the so-called pseudo-gap state which is adjacent to the superconducting phase. In Sr₃Ru₂O₇, we succeeded in observing the magnetic field effects on LDOS across the metamagnetic transition as well as the novel surface superstructure. These observations provide useful information to understand the effects of electron correlation in transitionmetal oxides.