Magnetism, conductivity, and superconductivity of molecular materials are discussed on the basis of extended Hubbard᎐Peierls Hamiltonians, which involve Ž . Ž . four parameters; transfer integral T , electron-lattice interaction W , and on-site and Ž . intersite Coulomb interactions U, V . The four-component spinor is introduced to define Ž order parameters which characterize four different electronic states charge density wave, . spin density wave, singlet and triplet superconductivities in a unified fashion. Several intermediate regions in these parameters are interesting and important from current theoretical reasons. Many experimental results clearly show the importance of intermediate correlation regimes for active controls of these states by chemical modifications and by external fields such as high pressure. Several model Hamiltonians such as CT and t᎐J models are derived for elucidation of potential electronic properties of molecule-based materials. Recent computational results based on the t᎐J model are utilized to rationalize our J model for spin-mediated superconductivity. Possibilities of magnetic conductors, charge-andror spin-mediated superconductors, and photoinduced superconductors instead of the charge-mediated Little model are examined in the intermediate region of several metal᎐insulator transitions. Possible candidates are also proposed on the basis of various circumstantial experimental results. Implications of the calculated results are finally discussed in relation to the recent development of the intersection area among conducting, magnetic, and optical molecular materials.