Manganese oxides with perovskite structure exhibit many interesting properties. Recently colossal magnetoresistance (CMR) was observed in these oxides. They show extremely large change in electrical resistance in response to applied magnetic fields. This property has lots of technological relevance for the development of magnetic memory and switching devices. These oxides also show transitions from antiferromagnet to ferromagnet coupled with charge-order to charge-nonorder transition. In this dissertation we examine the electronic origin of these phenomena of lanthanum manganites by studying a model electronic Hamiltonian, which includes double-exchange, super-exchange, and Hubbard terms, using a combination of Hartree-Fock approximation and an exact diagonalization scheme. The existence of "canted" spin order is investigated at zero temperature. We find that the double-exchange mechanism does not always lead to a canted magnetic state, even for small carrier concentration. The canting may be suppressed in these compounds for the typical electronic parameters. We study the charge ordering and magnetic transitions in the perovskites by solving the Hamiltonian both at zero and finite temperature. At zero temperature as we increase the strength of the extended-Hubbard repulsion $(U\sb1), $ a first-order transition from a charge-non-ordered metallic ferromagnet (FN) to a charge-ordered, insulating antiferromagnet (AFO) is obtained. The AFO-FN transition is also obtained by increasing the temperature T. The melting of charge ordering as a function of temperature, doping concentration and magnetic field is also examined. Different phases are obtained as a function of temperature and doping concentration. These are in qualitative agreement with experimental data. We study the electronic structures of pyrochlores by the density-functional LMTO method and show that the double-exchange mechanism is relevant for these compounds as well.