The interplays among various orderings of the spin, charge and orbital degrees of freedom in a broad spectrum of crystalline structures produce a number forms of symmetry-breaking patterns of spatial inversion, time-reversal and gauge symmetries, leading to exciting emergent phenomena in strongly-correlated electron systems and promising a variety of potential applications. The main objective of this dissertation is synthesis, characterization and terahertz study of metal oxides, which particularly refers to the transition metal oxide of ZnO and multiferroic BiFeO3 materials. Polaronic transport and magnetic properties of Ag- and Cu-doped ZnO bulk ceramics are studied in details. Terahertz time-domain spectroscopy is employed to investigate the complex conductivity of Ag- and Cu-doped ZnO thin films, as well as the THz response of the BiFeO3 thin film on SrLaAlO4. Further, a novel ultrafast approach is presented which seeks to directly measuring the reversal rate (and hence the magnetoelectric coupling) by measuring the time-resolved magneto-optic Faraday and Kerr rotation.